interfacial adsorption phenomena of the three dimensional three state potts model the authors study the interfacial adsorption phenomena of the three state ferromagnetic potts model on the simple cubic lattice by the monte carlo method finite size scaling analyses of the net adsorption yield evidence of the phase transition being of first order and kbtc j 1 8166 2

generalized bayesian information criterion for source enumeration in array processing we investigate the problem of enumerating source signals impinging on an array of sensors in an information theoretic framework the conventional bayesian information criterion bic does not yield satisfactory performance for this problem because it only considers the density of the observations in order to remedy the limitations of the bic we propose a generalized bayesian information criterion gbic rule by incorporating the density of the sample eigenvalues or corresponding statistics such a density contains extra information and complements the density of the observations in constructing the gbic as a result two different expressions for the gbic are suggested simulation results validate the superiority of the proposed gbic over the conventional bic in terms of correctly determining the number of sources while their computational costs are comparable

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

finite size scaling of the three state potts model on a simple cubic lattice finite size scaling is studied for the three state potts model on a simple cubic lattice we show that the specific heat and the magnetic susceptibility scale accurately as the volume the correlation length exhibits behaviors expected for a genuine first order transition the one extracted from the unsubtracted correlation function shows a characteristic finite size behavior whereas the physical correlation length that characterizes the first excited state stays at a finite value and is discontinuous at the transition point

finite size effects for the potts model with weak boundary conditions using the pirogov sinai theory we study finite size effects for the ferromagnetic q state potts model in a cube with boundary conditions that interpolate between free and constant boundary conditions if the surface coupling is about half of the bulk coupling and q is sufficiently large we show that only small perturbations of the ordered and disordered ground states are dominant contributions to the partition function in a finite but large volume this allows a rigorous control of the finite size effects for these weak boundary conditions in particular we give explicit formulae for the rounding of the infinite volume jumps of the internal energy and magnetization as well as the position of the maximum of the finite volume specific heat while the width of the rounding window is of order l d the same as for periodic boundary conditions the shift is much larger of order l 1 for strong boundary conditions the surface coupling is either close to zero or close to the bulk coupling the finite size effects at the transition point are shown to be dominated by either the disordered or the ordered phase respectively in particular it means that sufficiently small boundary fields lead to the disordered and not to the ordered gibbs state this gives an explicit proof of a van enter s result that the phase transition in the potts model is not robust

the potts model and flows ii many spin correlation function for pt i see ibid vol 19 p 411 1985 a graph theoretic analysis is made of the m spin correlation functions of the lambda state potts model in paper i the correlation functions for m 2 were expressed in terms of rooted mod lambda flow polynomials the authors introduce a more general type of polynomial the partitioned m rooted flow polynomial which plays a fundamental role in the calculation of the multispin correlation functions the m rooted equivalent transmissivities of tsallis and levy 1981 are interpreted in terms of percolation theory and are expressed as linear combinations of the above correlation functions

using the sphericity test for source detection with narrow band passive arrays a new sphericity test statistic is proposed for the complex case with a distribution that approaches the asymptotic chi squared distribution much faster than previously proposed statistics especially for situations in which the sources are very difficult to detect such as closely spaced or weak sources consequently the probability of a correct estimate is superior to those resulting from other sphericity tests the capability of this new sphericity test to detect closely space sources is examined and compared to the resolution capabilities of bearing estimation algorithms as well as other well known source detection algorithms

critical behaviour of the two dimensional potts model with a continuous number of states a finite size scaling analysis we investigate the critical behaviour of the two dimensional q state potts model using finite size scaling and transfer matrix methods for the continuous transition range 0 these results for continuous q were obtained from a transfer matrix constructed for a generalized whitney polynomial representing the potts models an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed

iteration inequalities of the maslov type index theory with applications abstract in this paper by using the index theory introduced by y long in 1999 pacific j math 187 113 149 in particular the splitting numbers maslov type mean index and the homotopy component of symplectic matrix we establish various inequalities of the maslov type index theory for iterations of symplectic paths starting from the identity as an application these results are used to study rabinowitz conjecture on the prescribed minimal period solution problem of nonlinear hamiltonian systems

closed characteristics on partially symmetric compact convex hypersurfaces in r2n abstract in this paper we study the multiplicity of closed characteristics on partially symmetric convex compact hypersurfaces in r 2n the main ingredient of the proof is a new p index function and its iteration theory for symplectic matrix paths and some symplectic orthogonal matrix p this theory yields estimates on this multiplicity via index estimates for a new type of iterations of any symplectic matrix path 0 sp 2n defined by t p t p for any t 0

the partition function zeros in the one dimensional q state potts model the zeros of the partition function in the one dimensional q state potts model with arbitrary and continuous q or 0 have been studied using a transfer matrix the location of zeros and the yang lee edge singularity have been analysed and two different regimes corresponding to q 1 and q 1 have been observed a duality relation has also been derived which relates the zeros in the complex field plane to those in the complex temperature plane

transfer matrices and partition function zeros for antiferromagnetic potts models vi square lattice with extra vertex boundary conditions we study using transfer matrix methods the partition function zeros of the square lattice q state potts antiferromagnet at zero temperature square lattice chromatic polynomial for the boundary conditions that are obtained from an m n grid with free boundary conditions by adjoining one new vertex adjacent to all the sites in the leftmost column and a second new vertex adjacent to all the sites in the rightmost column we provide numerical evidence that the partition function zeros are becoming dense everywhere in the complex q plane outside the limiting curve mathcal b infty mathrm sq for this model with ordinary e g free or cylindrical boundary conditions despite this the infinite volume free energy is perfectly analytic in this region

systems with logarithmic specific heat finite size scaling a detailed study is presented of the finite size scaling in systems with vanishing critical exponent alpha which usually have logarithmic specific heat singularity the appropriate form of the finite size hyperuniversality is established recent results on complex temperature plane zeros of the partition function are extended to the alpha 0 case

iteration inequalities of the maslov p index theory with applications abstract in this paper the p splitting numbers and p mean index for a symplectic path starting from the identity with p s p 2 n are defined first and then by using the maslov p index theory for a symplectic path various inequalities of the maslov p index theory for iterations of symplectic paths starting from the identity are established as an application these results are used to study the minimal period problem of p symmetric periodic solution of nonlinear autonomous hamiltonian systems

the phase diagram of the o n model we investigate the properties of the zero field o n model on the honeycomb lattice outside the range of presently available exact solutions to this purpose we make use of finite size scaling and transfer matrix techniques our results confirm the expected phase diagram of the o n model in the range 0 n 2 it consists of a disordered phase separated by a second order transition from a low temperature phase with algebraically decaying correlations we confirm that in this low temperature phase the exponents are independent of the temperature more significantly we find evidence for this same universal behaviour even in the case n 2 this contrasts with the temperature dependent exponents of the generic xy model our numerical evidence in this case is supported by arguments based on a mapping from the o n 2 model to the ashkin teller model on the triangular lattice furthermore our results agree with the absence of a phase transition for n 2 for negative values of n we observe unphysical singularities in the free energies of finite systems

series analysis of the 3 state potts model in 2 1 dimensions both high temperature and low temperature series are used to locate and characterize the first order transition in the 3 state potts model in 2 1 dimensions on both square and triangular lattices estimates are presented for the vacuum energy latent heat magnetization susceptibility and mass gap at the transition the spontaneous magnetization and latent heat appear to display an approximate universality at this weak first order transition

bootstrap multiple tests applied to sensor location a method for finding optimal locations of vibration sensors within a group of sensors for detecting knock in combustion engines is proposed it differs from other techniques in that only signal processing and statistical tests are used the method is based on linearly predicting the in cylinder pressure in a combustion chamber from the output signals of a group of vibration sensors being distributed on the engine wall the irrelevancy of a sensor in the group is characterized by the closeness to zero of a coherence gain explained by this sensor at some frequencies of interest we formulate multiple hypotheses define suitable statistics approximate their sampling distributions by the nonparametric bootstrap method and construct the generalized sequentially rejective bonferroni multiple test the level of accuracy of bootstrap tests is superior to that of asymptotic tests provided the test statistic used is asymptotically pivotal to achieve pivoting we transform the test statistic into a variance stable scale where we use a bootstrap technique to approximate the variance stabilizing transformation simulations results as well as results of an experiment performed on a test bed with a four cylinder engine emphasize the applicability of the method

estimation of the number of sources in unbalanced arrays via information theoretic criteria estimating the number of sources impinging on an array of sensors is a well known and well investigated problem a common approach for solving this problem is to use an information theoretic criterion such as minimum description length mdl or the akaike information criterion aic the mdl estimator is known to be a consistent estimator robust against deviations from the gaussian assumption and nonrobust against deviations from the point source and or temporally or spatially white additive noise assumptions over the years several alternative estimation algorithms have been proposed and tested usually these algorithms are shown using computer simulations to have improved performance over the mdl estimator and to be robust against deviations from the assumed spatial model nevertheless these robust algorithms have high computational complexity requiring several multidimensional searches in this paper which is motivated by real life problems a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken an mdl type estimator that is robust against deviation from assumption of equal noise level across the array is studied the consistency of this estimator even when deviations from the equal noise level assumption occur is proven a novel low complexity implementation method avoiding the need for multidimensional searches is presented as well making this estimator a favorable choice for practical applications

the 3 state potts model in 2 1 dimensions the 3 state potts model in 2 1 dimensions is studied using series and monte carlo methods high temperature series for the vacuum energy mass gap and susceptibility are computed on the square and triangular lattices using linked cluster expansions monte carlo estimates are obtained by the stochastic truncation method the model is found to undergo a weak first order transition as in the euclidean version of the model

on the eight vertex model and related models a new method and some new results abstract we report recent work on classical models in two dimensions and related one dimensional quantum hamiltonians which are exactly solvable by using inversion relations for the transfer matrix of such models we have developed a new method to calculate all its eigenvalues and to determine the eigenstates in the thermodynamic limit for the 8 vertex model this leads to a complete classification of the excited states for the self dual q state potts model we derive the excitations of the diagonal transfer matrix and determine the diagonal correlation length explicitly we also report on the exact solution of the biquadratic spin 1 quantum antiferromagnet

transfer matrix test of the two cell mean field renormalization group abstract a transfer matrix approach has been worked out to test the predictions of the two cell mean field renormalization group mfrg for the square ising cells with linear size up to l 11 the convergence of the finite size critical couplings towards the exact value both for mfrg and for the cluster mfa is shown and the limit of the ratio yh yt consistent with the corresponding universal value is found applications within mfa are also briefly discussed

finite size scaling of critical cumulants near the ferromagnetic phase boundary abstract we employ the recently proposed scaling theory for first order transitions to derive a detailed prediction for the large argument behaviour of the critical point scaling function of the reduced fourth order cumulant g l 4 2 2 3 correct up to a term exponentially small in l t

higher dimensional temperley lieb algebras a category which generalizes to higher dimensions many of the features of the temperley lieb category is introduced

finite size effects and phase transition in the three dimensional three state potts model the three state potts model in three dimensions is studied by monte carlo and finite size scaling techniques using a histogram method recently proposed by ferrenberg and swendsen the finite size dependence for the maximum of the specific heat is found to scale with the volume of the system indicating that the phase transition is of first order the value of the latent heat per spin and the correlation length at the transition are estimated

static and dynamic critical phenomena of the two dimensional q state potts model theq state potts model on the square lattice is studied by monte carlo simulation forq 3 4 5 6 very good agreement is obtained with exact results of kiharaet al and baxter for energy and free energy at the critical point critical exponent estimates forq 3 are 0 4 0 1 1 45 in rough agreement with high temperature series extrapolation and real space renormalization group methods the transition forq 5 6 is found to be a very weakly first order transition i e pronounced pseudocritical phenomena occur specific heat susceptibility etc nearly diverge at the first order transition temperature dynamics is associated to the model in the same way as for the kinetic ising model and the nonlinear slowing down of the order parameter and of the energy is studied the dynamic exponent is estimated to be zv 1 9 within our accuracy noq dependence is detected the relaxation is found to be consistent with dynamic scaling predictions and dynamic scaling functions associated with the nonlinear relaxation are estimated

a new obstruction to embedding lagrangian tori n let 2n be endowed with the canonical symplectic form a i 1 dxi dy i and consider a lagrangian embedding of a compact manifold j l r 2 a a well known result due to g r o m o v g states that the cohomology class of a in h z e 2 l is non zero we identify l with its image in r2 an equivalent assertion is that the liouville form 2 y 7 1 xldy i pulls back to a closed form j 2 on l whose cohomology class does not vanish g r o m o v s proof uses subtle properties of holomorphic maps into c he shows that there is always a holomorphic disk a in c with boundary in l on such a disk a is positive hence sa a soa 2 0 in this paper we shall only consider the case l t and give an elementary proof of gromov s result elementary should be understood in the sense of number theory that is without using holomorphic functions in fact our result is somewhat more precise and can be stated as follows

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

the gauge potts model on a generalized bethe lattice the q states gauge potts model is exactly solved on a special infinite dimensional lattice which is a bethe lattice of plaquettes the critical properties are studied the model exhibits a first order transition for any number of states q and coordination number gamma 1 the critical values of coupled constant beta c is shown to be in a good agreement with known results

irrationally elliptic closed characteristics on compact convex hypersurfaces in r6 abstract in this paper let r 6 be a compact convex hypersurface which carries exactly three geometrically distinct closed characteristics we prove that at least two of them must be irrationally elliptic

performance analysis of the decentralized eigendecomposition and esprit algorithm in this paper we consider performance analysis of the decentralized power method for the eigendecomposition of the sample covariance matrix based on the averaging consensus protocol an analytical expression of the second order statistics of the eigenvectors obtained from the decentralized power method which is required for computing the mean square error mse of subspace based estimators is presented we show that the decentralized power method is not an asymptotically consistent estimator of the eigenvectors of the true measurement covariance matrix unless the averaging consensus protocol is carried out over an infinitely large number of iterations moreover we introduce the decentralized esprit algorithm which yields fully decentralized direction of arrival doa estimates based on the performance analysis of the decentralized power method we derive an analytical expression of the mse of doa estimators using the decentralized esprit algorithm the validity of our asymptotic results is demonstrated by simulations

the temperature exponent of the n component cubic model we have applied transfer matrix and finite size scaling techniques to obtain critical couplings and temperature exponents for n component cubic models on the square lattice in these calculations n enters as a continuously variable parameter the results for the temperature exponent are in agreement with recent predictions

a tree decomposed transfer matrix for computing exact potts model partition functions for arbitrary graphs with applications to planar graph colourings combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs the algorithm is particularly efficient in the case of planar graphs we illustrate it by computing the potts model partition functions and chromatic polynomials the number of proper vertex colourings using q colours for large samples of random planar graphs with up to n 100 vertices in the latter case our algorithm yields a sub exponential average running time of a substantial improvement over the exponential running time exp 0 245n provided by the hitherto best known algorithm we study the statistics of chromatic roots of random planar graphs in some detail comparing the findings with results for finite pieces of a regular lattice

existence of multiple periodic orbits of hamiltonian systems on positive type hypersurfaces in r2n abstract this paper deals with the fixed energy problem of hamiltonian systems in r 2n the main result is an existence theorem of multiple periodic orbits for hamiltonian vector fields on a class of contact type but not necessarily star shaped hypersurfaces this is the first multiplicity result for hypersurfaces that are more general than star shaped ones the main result is achieved by using critical point theory for a special hamiltonian function and central gravity of the proof relies on a delicate construction of such hamiltonian function

structure of the partition function and transfer matrices for the potts model in a magnetic field on lattice strips we determine the general structure of the partition function of the q state potts model in an external magnetic field z g q v w for arbitrary q temperature variable v and magnetic field variable w on cyclic mobius and free strip graphs g of the square sq triangular tri and honeycomb hc lattices with width ly and arbitrarily great length lx for the cyclic case we prove that the partition function has the form z lambda l y times l x q v w sum d 0 l y tilde c d mathrm tr t z lambda l y d m where denotes the lattice type tilde c d are specified polynomials of degree d in q t z lambda l y d is the corresponding transfer matrix and m lx lx 2 for sq tri hc respectively an analogous formula is given for mobius strips while only t z lambda l y d 0 appears for free strips we exhibit a method for calculating t z lambda l y d for arbitrary ly and give illustrative examples explicit results for arbitrary ly are presented for t z lambda l y d with d ly and d ly 1 we find very simple formulas for the determinant mathrm det t z lambda l y d we also give results for self dual cyclic strips of the square lattice

a first order phase transition in the three dimensional four state antiferromagnetic potts model studies the four state antiferromagnetic potts model with next nearest neighbour ferromagnetic interactions on the simple cubic lattice by the monte carlo method the ratio j2 j1 of the strength of the next nearest neighbour interactions to that of the nearest neighbour interactions is to be 10 the author analyses the finite size effects of the energy the specific heat the fourth order cumulant the magnetization the susceptibility and the effective transition temperatures with the help of the finite size scaling theory the author concludes that the transition of the model is assigned to be of first order

critical behaviour of the 1d q state potts model with long range interactions the critical behaviour of the one dimensional q state potts model with long range interactions decaying with distance r as r 1 sigma has been studied in the wide range of parameters 0 sigma or 1 and 1 16 or q or 64 a transfer matrix has been constructed for a truncated range of interactions for integer and continuous q and finite range scaling has been applied results for the phase diagram and the correlation length critical exponent are presented

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

the o n model on the triangular lattice to find critical points of o n models on the triangular lattice we apply two methods first we investigate the yang baxter equations on the triangular lattice we find only solvable points directly related to those for the square lattice second we construct intersections with the potts model this yields eight branches of critical points parametrized by n we establish the equivalence of these branches with the known critical points of the o n model on the square lattice transfer matrix calculations are performed to obtain the conformal anomaly and the thermal exponent of these branches these results include a numerical analysis of a q 3 potts tricritical point we find analytic relations between potts and o n models as well as among o n models with different values of n and among potts models with different values of q

stable closed characteristics on partially symmetric convex hypersurfaces abstract let n be a positive integer and p diag in i in i for some integer 0 n in this paper we prove that for any convex compact smooth hypersurface in r2n with n 2 there always exists at least one closed characteristic on which possesses at least 2n 4 floquet multipliers on the unit circle of the complex plane provided is p symmetric i e x implies px

on an algebraic approach to higher dimensional statistical mechanics we study representations of temperley lieb algebras associated with the transfer matrix formulation of statistical mechanics on arbitrary lattices we first discuss a new hyperfinite algebra the diagram algebra d underset raise0 3em hbox smash scriptscriptstyle n q which is a quotient of the temperley lieb algebra appropriate for potts models in the mean field case and in which the algebras appropriate for all transverse lattice shapesg appear as subalgebras we give the complete structure of this subalgebra in the case hat a n potts model on a cylinder the study of the full temperley lieb algebra of graphg reveals a vast number of infinite sets of inequivalent irreducible representations characterized by one or more complex parameters associated to topological effects such as links we give a complete classification in the hat a n case where the only such effects are loops and twists

quenched bond dilution in two dimensional potts models we report a numerical study of the bond diluted two dimensional potts model using transfer matrix calculations for different numbers of states per spin we show that the critical exponents at the random fixed point are the same as in self dual random bond cases in addition we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin spin correlation function in the cylinder geometry we show that the behaviour is fully compatible with the one observed in the random bond case confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder dilution self dual binary random bond self dual continuous random bond

synergistic development of differential approximants and the finite lattice method in lattice statistics several decades of parallel developments in the calculation and analysis of series expansions for lattice statistics have led to many new insights into critical phenomena these studies have centered on the use of the finite lattice method for series expansions in lattice statistics and the use of differential approximants in analysing such series one of these strands of research ultimately led to the result that a number of unsolved lattice statistics problems cannot be expressed as d finite functions somewhat ironically given power and success of differential approximants in analysing series neither the assumed functional form nor any finite generalisation thereof can fit such cases exactly

morse type index theory for flows and periodic solutions for hamiltonian equations an index theory for flows is presented which extends the classical morse theory for gradient flows on compact manifolds the theory is used to prove a morse type existence statement for periodic solutions of a time dependent periodic in time and asymptotically linear hamiltonian equation

crossover finite size scaling at first order transitions in a recent paper we developed a method which allows one to control rigorously the finite size behavior in long cylinders near first order phase transitions at low temperature here we apply this method to asymmetric transitions with two competing phases and to theq state potts model as a typical model of a temperature driven transition whereq low temperature phases compete with one high temperature phase we obtain the finite size scaling of the firstn eigenvalues wheren is the number of competing phases of the transfer matrix in a periodic box of volumel l t and as a corollary the finite size scaling of the shape of the order parameter in a hypercubic box t l the infinite cylinder t and the crossover regime from hypercubic to cylindrical scaling for the two phase case n 2 we find that the crossover length l is given by o lw exp lv where is the inverse temperature is the surface tension and w 1 2 if v 1 2 whilew 0 if v 1 2 for the standard ising model we also consider free boundary conditions showing that l exp lv o lv 1 for any dimension v 1 2 for v 1 2 we finally discuss a class of boundary conditions which interpolate between free corresponding to the interpolating parameter g 0 and periodic boundary conditions corresponding to g 1 finding that l o lw exp lv withw 0 forg 0 andw 1 2 for 0 g 1

collapse of a polymer in two dimensions abstract we numerically investigate the influence of self attraction on the critical behaviour of a polymer in two dimensions by means of an analysis of finite size results of transfer matrix calculations the transfer matrix is constructed on the basis of the o n loop model in the limit n 0 it yields finite size results for the magnetic correlation length of systems with a cylindrical geometry a comparison with the predictions of finite size scaling enables us to obtain information about the phase diagram as a function of the chemical potential of the loop segments and the strength of the attractive potential results for the magnetic scaling dimension can be interpreted in terms of known universality classes in particular when the attractive potential is increased we observe the crossover between the polymer critical behaviour of the self avoiding walk type to behaviour described earlier for the theta point

ising model with two spin interactions and three spin interactions on a square lattice abstract an ising model with two spin interactions in one direction and four spin interactions on the smallest plaquettes is investigated on the square lattice the part of the two spin interactions is essential to determine the nature of the phase transition of the model the system with nearest neighbour interactions has no phase transition the one with next nearest neighbour interactions has a spontaneous magnetization and belongs to the same class of universality as the eight vertex model the one with third neighbour interactions has no spontaneous magnetization but belongs to the same class of universality as onsager s lattice and so on

on the duality relation for correlation functions of the potts model we prove a recent conjecture on the duality relation for correlation functions of the potts model for boundary spins of a planar lattice specifically we deduce the explicit expression for the duality of the n site correlation functions and establish sum rule identities in the form of the mobius inversion of a partially ordered set the strategy of the proof is by first formulating the problem for the more general chiral potts model the extension of our consideration to the many component potts models is also given

equivariant morse theory for starshaped hamiltonian systems soit une hypersurface en forme d etoile dans r 2n le probleme de trouver des caracteristiques fermees de peut se reduire classiquement a un probleme variationnel ceci conduit a etudier une fonctionnelle s 1 equivariante sur un espace de hilbert

critical behaviour and conformal anomaly of the o n model on the square lattice finite size scaling and transfer matrix techniques are used to determine the conformal anomaly and critical exponents of o n models on the square lattice these calculations were performed on five branches of critical points parametrised by n the results for two of the branches agree with the known universal properties of the o n model as derived for the honeycomb lattice finite size convergence is poor for most of the third branch so that in this case the classification in terms of known models is uncertain the authors data show that the fourth branch can be interpreted in terms of a combination of a low temperature o n and a critical ising model finally the numerical results for the o n model on the remaining branch agree accurately with the known results for the low temperature o n 1 model they prove this equivalence by means of an exact mapping

two dimensional scaling in magnetic systems with non integer characteristic lengths we studied the ferromagnetic ising model on two dimensional finite systems with non integer characteristic lengths first we considered very long strips with a finite number i of complete rows and one partially filled row with probability x which is the two dimensional version of a layer by layer growth at fixed temperature when the characteristic length l i x increases the free energy per spin the specific heat and the magnetic susceptibility oscillate attaining relative extremes at integer l the oscillations in the free energy are interpreted as surface corrections related to the oscillations in the mean coordination number finite size scaling relations are not satisfied with continuous l but still hold for fixed x and variable i where the differences of mean widths are integers for fixed x the fits of the free energy give the conformal anomaly with very good accuracy we also studied strips with discretized gaussian distributions of widths with non integer means l and rms deviation in these structures the thermodynamic quantities vary monotonically with continuous l but some methods for calculating critical exponents do not work properly when generalized to continuous l we also obtain with good accuracy in these systems we discuss the possible implications of our results to real systems behaviour

correlation length of the three state potts model in three dimensions a monte carlo study is carried out for the three state potts model in three dimensions the correlation length is shown to remain finite and to be discontinuous at the transition point it is also shown that the transition exhibits genuine first order characteristics in all aspects

effects of interface width scaling and spatial correlations on ising systems with rough boundaries we studied the ferromagnetic ising model on two dimensional systems with rough boundaries and several thickness distributions first we considered very long strips with discretized gaussian distributions of widths with mean 3 l 12 systems with fixed interface width w and with increasing roughness w l with 0 1 were analysed we also considered strips with columns heights correlations where the difference in the heights of neighbouring columns was 0 or 1 with 0 0 5 free energies per spin fl and initial susceptibilities l were calculated using transfer matrix techniques at the critical temperature of the two dimensional ising model the scaling of fl and of the finite size estimates of the ratio of exponents l was analysed in systems with small and slowly increasing w 0 2 correlated or not extrapolations of fl and l to l give accurate estimates of the critical parameters f and in systems with rapidly increasing roughness the deviations of those estimates from the exact values indicate the presence of large corrections in finite size scaling relations the comparison of systems with nearly the same shows that spatial correlations have no systematic effect on corrections to scaling it suggests the reliability of uncorrelated models or related approximate systems for the description of scaling properties of thin magnetic films and other low dimensional structures

the number of link and cluster states the core of the 2d q state potts model due to fortuin and kastelyin the q state potts model has a representation as a sum over random graphs generalizing the potts model to arbitrary q is based on this representation a key element of the random cluster representation is the combinatorial factor which is the number of ways to form distinct clusters consisting of totally edges we have devised a method to calculate from monte carlo simulations

index iteration theories for periodic orbits old and new abstract in this paper we give a survey of the index iteration theories developed for periodic solution orbits of hamiltonian systems in treating various problems from 1950s up to now including some recent developments and some of their applications to periodic solution problems

oblique projection based enumeration of mixed noncoherent and coherent narrowband signals in many application scenarios the signals impinging on the array of sensors comprise the noncoherent uncorrelated and or partially correlated signals and the coherent signals with several groups due to multipath propagation in this paper we consider the problem of estimating the number of noncoherent narrowband signals and that of coherent narrowband signals with multiple groups impinging on a planar sensor array composed of two parallel uniform linear arrays ulas and an oblique projection based enumerator for the mixed signals opems is proposed by utilizing the qr decomposition based ratio criterion qrrc for rank determination of a matrix in the opems the number of noncoherent signals and that of coherent signals in each group are estimated separately where only the elevation angles of noncoherent signals are estimated to isolate the coherent signals from the noncoherent ones and the computationally intensive and time consuming eigendecomposition procedure is avoided the consistency of the proposed opems is analyzed and its effectiveness is verified through numerical examples

spanning forests and the q state potts model in the limit q 0 we study the q state potts model with nearest neighbor coupling v e j 1 in the limit q v 0 with the ratio w v q held fixed combinatorially this limit gives rise to the generating polynomial of spanning forests physically it provides information about the potts model phase diagram in the neighborhood of q v 0 0 we have studied this model on the square and triangular lattices using a transfer matrix approach at both real and complex values of w for both lattices we have computed the symbolic transfer matrices for cylindrical strips of widths 2 l 10 as well as the limiting curves b of partition function zeros in the complex w plane for real w we find two distinct phases separated by a transition point w w0 where w0 1 4 resp w0 0 1753 0 0002 for the square resp triangular lattice for w w0 we find a non critical disordered phase that is compatible with the predicted asymptotic freedom as w for w w0 our results are compatible with a massless berker kadanoff phase with central charge c 2 and leading thermal scaling dimension xt 1 2 marginally irrelevant operator at w w0 we find a first order critical point the first derivative of the free energy is discontinuous at w0 while the correlation length diverges as w w0 and is infinite at w w0 the critical ehavior at w w0 seems to be the same for both lattices and it differs from that of the berker kadanoff phase our results suggest that the central charge is c 1 the leading thermal scaling dimension is xt 1 0 and the critical exponents are 1 d 1 2 and 1

transfer matrix computation of generalized critical polynomials in percolation percolation thresholds have recently been studied by means of a graph polynomial pb p henceforth referred to as the critical polynomial that may be defined on any periodic lattice the polynomial depends on a finite subgraph b called the basis and the way in which the basis is tiled to form the lattice the unique root of pb p in 0 1 either gives the exact percolation threshold for the lattice or provides an approximation that becomes more accurate with appropriately increasing size of b initially pb p was defined by a contraction deletion identity similar to that satisfied by the tutte polynomial here we give an alternative probabilistic definition of pb p which allows for much more efficient computations by using the transfer matrix than was previously possible with contraction deletion we present bond percolation polynomials for the 4 82 kagome and 3 122 lattices for bases of up to respectively 96 162 and 243 edges much larger than the previous limit of 36 edges using contraction deletion we discuss in detail the role of the symmetries and the embedding of b for the largest bases we obtain the thresholds pc 4 82 0 676 803 329 pc kagome 0 524 404 998 pc 3 122 0 740 420 798 comparable to the best simulation results we also show that the alternative definition of pb p can be applied to study site percolation problems this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

corner exponents in the two dimensional potts model the critical behavior at a corner in two dimensional ising and three state potts models is studied numerically on the square lattice using transfer operator techniques the local critical exponents for the magnetization and the energy density for various opening angles are deduced from finite size scaling results at the critical point for isotropic or anisotropic couplings the scaling dimensions compare quite well with the values expected from conformal invariance provided the opening angle is replaced by an effective one in anisotropic systems

approximation schemes for finite lattices two algorithms are formulated for systematically truncating the set of basis states required in lattice hamiltonian calculations thus allowing larger lattice abort sizes to be treated they are tested for the case of the 1 1 dimensional ising model it is shown that smoothly convergent finite lattice sequences are obtained which can successfully the extrapolated to the bulk limit the authors point out the relevance of the technique for lattice calculations in higher dimensions

convergence and extrapolation in finite size scaling renormalization abstract finite size renormalization technique is studied by examining a test model which is exactly solvable and the problem of lattice animals and self avoiding walks bulk estimates of the leading irrelevant rg eigenvalue are found and compared with independent estimates from finite size data we introduce an extrapolation technique which is applicable to non monotonic sequences of exponent approximants

multiple phase coexistence and the scaling transformation it is shown that a simple extension of the finite size scaling method in the theory of critical phenomena can yield a sequence of approximants to any point subset of the interaction parameter space where multiple phase coexistence is possible the method is illustrated by an application to the three four and five state potts models and even in its lowest order of approximation is able to distinguish the difference in the zero field critical behaviour between the five state and the three and four state models

latent heats from finite size scaling a method of obtaining the latent heat at a first order transition from finite lattice matrix elements is discussed and demonstrated for the case of the 1 1 d potts model the method is shown to provide smoothly convergent finite lattice sequences the structure of the finite lattice hamiltonian eigenvalues is exhibited and a characteristic signal of the first order transition is proposed the finite size scaling behaviour at the transition is also discussed

convergence of finite size scaling renormalisation techniques abstract the rate of convergence of the transfer matrix finite size scaling or phenomenological renormalisation method is studied it is shown both heuristically and numerically that the convergence of estimates for exponents etc is governed asymptotically by the leading irrelevant variable scaling exponent the more rapid apparent convergence rates observed in many practical calculations for two dimensional lattices of widths up to ten lattice spacings are attributed to cancellation between various correction terms

finite size scaling for first order phase transitions rigorous results abstract recent rigorous results on finite size effects for lattice models are reviewed we consider symmetric and asymmetric first order phase transitions in cubic and cylindrical geometries and discuss the determination of transition points from finite size data

source enumeration in array processing using a two step test we investigate the problem of enumerating source signals impinging on an array of sensors given noisy limited observations the assumption of a large sample size is indispensable for most of the existing approaches so that they suffer significant performance degradation when only a small number of samples is available random matrix theory can capture the asymptotic distributions of the eigenvalues accurately and provide good approximations even for a finite sample size in this paper we take into account the relationship and distributions of the noise and signal eigenvalues based on random matrix theory and derive a simple two step test numerical simulations demonstrate that it is capable of correctly determining the number of sources in the case of small sample sizes

critical behaviour and logarithmic corrections of a quantum model with three spin interaction extended finite size scaling and series expansion methods are used to determine the critical properties of the one dimensional quantum ising model with three spin interaction by supposing the presence of logarithmic corrections the universality class of the model is investigated the results obtained by different methods support the conjecture that the model belongs to the same universality class as the four state potts model

a transfer matrix for the backbone exponent of two dimensional percolation rephrasing the backbone of two dimensional percolation as a monochromatic path crossing problem we investigate the latter by a transfer matrix approach conformal invariance links the backbone dimension db to the highest eigenvalue of the transfer matrix t and we obtain the result db 1 6431 0 0006 for a strip of width l t is roughly of size 23l but we manage to reduce it to l we find that the value of db is stable with respect to inclusion of additional blobs tangent to the backbone in a finite number of points

hyperbolic closed characteristics on compact convex smooth hypersurfaces inr2n in this paper we prove that on every compactc2hypersurface inr2nbounding a convex set with non empty interior either there exists a sequence of variationally visible hyperbolic closed characteristcs with their minimal periods tending to infinity or there exists at least one variationally visible nonhyperbolic closed characteristic

detection of sources using bootstrap techniques source detection in array processing can be viewed as a test for equality of eigenvalues such a test is proposed based on a multiple test procedure that considers all pairwise comparisons between eigenvalues using the bootstrap to estimate the null distributions of the test statistics results in a procedure with minimal assumptions on the nature of the signal simulations show that the proposed test is superior to information theoretic criteria such as the mdl which are based on gaussian signals and large sample sizes performance in most cases exceeds the more powerful sphericity test

flexible detection criterion for source enumeration in array processing two new procedures are proposed using random matrix theory to evaluate theoretically the performance of the bayesian information criterion bic for source enumeration in array processing the proposed procedures can predict precisely the estimation results of the bic also they shed light on the behavior of the bic in order to remedy the limitation of the bic that is the bic tends to underestimate the number of sources by one in most cases an extra parameter is introduced into the bic formulation which results in a new criterion for source enumeration referred to as the flexible detection criterion fdc by carefully choosing this parameter the fdc is capable of substantially reducing the probability of underestimation which is validated by theoretical analysis and simulations note that the fdc is consistent and has low computational complexity as the bic

finite size scaling at first and second order phase transitions of baxter wu model abstract using a finite size phenomenological theory we investigate the behavior of the baxter wu model for both first and second order transitions in order to distinguish between the two kinds of transition we study the finite size scaling behavior of the order parameter and the susceptibility of the model at the critical temperature the known critical exponents of the system govern the scaling behavior while below the critical temperature the scaling exponents are the dimensionality of the system the presented scaling theory for the baxter wu model is an appropriate generalization of the corresponding theory of binder and landau for the ising model binder and landau phys rev b 30 1984 1477 we perform numerical simulations using standard monte carlo techniques and we find that our results are in good agreement with theoretical predictions

surface induced finite size effects for first order phase transitions we consider classical lattice models describing first order phase transitions and study the finite size scaling of the magnetization and susceptibility in order to model the effects of an actual surface in systems such as small magnetic clusters we consider models with free boundary conditions for a field driven transition with two coexisting phases at the infinite volume transition pointh h t we prove that the low temperature finite volume magnetizationmfree l h per site in a cubic volume of sizel d behaves like m free l h frac m m 2 frac m m 2 tanh left frac m m 2 l d h h chi l right o left frac 1 l right whereh x l is the position of the maximum of the finite volume susceptibility andm are the infinite volume magnetizations ath h t 0 andh h t 0 respectively we show thath x l is shifted by an amount proportional to 1 l with respect to the infinite volume transition pointh t provided the surface free energies of the two phases at the transition point are different this should be compared with the shift for periodic boundary conditions which for an asymmetric transition with two coexisting phases is proportional only to 1 l2d one can consider also other definitions of finite volume transition points for example the positionh u l of the maximum of the so called binder cumulantufree l h whileh u l is again shifted by an amount proportional to 1 l with respect to the infinite volume transition pointh t its shift with respect toh l is of the much smaller order 1 l2d we give explicit formulas for the proportionality factors and show that in the leading 1 l2d term the relative shift is the same as that for periodic boundary conditions

monte carlo method for critical systems in infinite volume the planar ising model in this paper we propose a monte carlo method for generating finite domain marginals of critical distributions of statistical models in infinite volume the algorithm corrects the problem of the long range effects of boundaries associated to generating critical distributions on finite lattices it uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of holographic boundary condition that encodes the presence of an infinite volume beyond it we check the quality of the distribution obtained in the case of the planar ising model by comparing various observables with their infinite plane prediction we accurately reproduce planar two three and four point of spin and energy operators we also define a lattice stress energy tensor and numerically obtain the associated conformal ward identities and the ising central charge

a family of methods for the solution of lattice models abstract we discuss a family of methods for evaluating the thermodynamic functions for a class of lattice models that includes the ising model it is shown that the usual transfer matrix method can be considered as a member of the family some typical members of this family are also introduced furthermore we are concerned with the acceleration of these methods for this reason an extra linear extrapolation algorithm which is based on the member of this family related to the transfer matrix method is presented by this algorithm not only can the bulk physical quantities be evaluated more precisely but also an approximation to the boundary thermodynamic quantities can be obtained a new expression for the boundary free energy of the ising model is derived in addition the convergence to the thermodynamic limit is proven for the scaling method presented by chorin some numerical results for the bulk and boundary thermodynamic functions of the ising model are included