conformal invariance and critical dynamics the author discusses the behaviour of dynamic correlation functions under conformal transformations in particular the exact form of the dynamic scaling function at the critical point for an arbitrary isotropic two dimensional model is obtained with either conserved or nonconserved order parameter

finite size scaling and universality in the spectrum of the quantum ising chain i periodic and antiperiodic boundary condition the spectrum of the quantum ising chain is studied in the finite size scaling limit for periodic and antiperiodic boundary conditions the finite size corrections are computed for all energy gaps the results of the model are used to test the privman fisher universality hypothesis and conformal theory at the critical point it is shown how to build the spectrum from the irreducible representations of the virasoro algebra in addition the author finds evidence for an unsuspected symmetry for systems both non critical and of finite size

the relation between amplitudes and critical exponents in finite size scaling the relation between critical exponents and the amplitude of the correlation length divergence at the critical point of two dimensional systems as a function of finite size is investigated and generalised in two ways correlations more general than those of order order type are included a form appropriate for anisotropic systems is proposed the authors present a exact results for the ising and gaussian models and b numerical results for the symmetric eight vertex baxter continuous q state potts and continuous n component cubic models

universal amplitudes in finite size scaling the antiperiodic 3d spherical model the antiperiodic 3d spherical model is studied on a hypercube lattice two sides of which are finite and the other infinite the universal correlation length finite size scaling amplitude in the conjectured relationship xi l a x is calculated exactly and found to be a 0 1361 which should be compared with the antiperiodic 3d ising model value of a approximately 0 12

universal finite size scaling amplitudes on a torus for the triangular ising lattice gas recently the author suggested studying the scaling properties of complex two dimensional phase transitions by calculating the universal amplitudes of interfacial free energies on a torus geometry employing monte carlo simulations he tests this method at the 3 3 phase transition in the ising lattice gas on a triangular lattice belonging to the chiral three state potts universality class the interfacial free energies for this lattice gas model can be written in terms of free energy differences between systems with different sizes the algorithm to calculate these free energy differences is presented using lattice sizes up to 18 18 and modest computing effort he finds that the universal amplitude a 1 220 02 in accordance with the exact analytical value for the non chiral three state potts model a 1 203291 which he determined earlier

pair correlations in the antiperiodic ising strip and conformal invariance an explicit formula for the spatial dependence of the pair correlation function in an ising strip with antiperiodic boundary conditions at the bulk critical temperature is given it follows from the conformal invariance approach of belevin et al 1986 and cardy 1986

monte carlo calculations of the conformal charge the conformal charge is an important quantity which characterizes the nature of the two dimensional phase transition we report a first attempt to use a new numerical method to calculate the conformal charge in this paper we apply our method to the 2 dimensional 4 continuous spin ising model by varying the parameters in the hamiltonian one can change continuously from the known gaussian limit to the ising limit it is well known that the critical points for these two systems are not in the same universality class we study this behavior for the gaussian model the single well 4 model the border model and the double well 4 model for a large lattice our results while giving a good general picture are not so far sufficient to differentiate whether the non gaussian cases studied belong to the ising model universality class or not further studies of other lattice sizes should serve to improve greatly our conclusions

conformal invariance and the critical behavior of the triplet xy quantum chain we introduce and study the critical properties of the tripletxy quantum chain this system is described in terms of three spin interactions and is the generalization of the standardxy quantum chain we show that this model with periodic boundaries has a local gauge invariance and can be described by the composition of two triplet ising models with general toroidal boundary conditions from this composition the phase diagram as well the conformai anomaly and critical exponents are determined by exploring their relations with the mass gap amplitudes predicted by conformai invariance

conformal invariance and self avoiding walks in restricted geometries the prediction of conformal invariance for the statistics of self avoiding random walks restricted to both semi infinite and wedge shaped geometries are tested by extrapolating exact enumerations close agreement is found both for the angular distribution of the end to end vector and for the dependence of the critical exponent gamma 2 on the opening angle of the wedge

conformal invariance and non universality in quantum spin chains with a defect the authors study quantum analogues of two dimensional ising models with a linear defect conformal invariance and scaling arguments are used to relate the exponent eta of the time correlation function of the spin at the defect to a finite chain mass gap ratio close agreement is found with the pertinent exact results

damage spreading in confined geometries and the influence of boundary conditions a monte carlo study of the ising ferromagnet the spreading of damage in the ising ferromagnet in two dimensional confined geometries of size l m l m close to the critical temperature is studied by means of computer simulations imposing both periodic and open boundary conditions along the m direction the influence of the interfaces between domains of spins having opposite orientation on the spreading of damage can be studied analyzing the spatio temporal evolution of the damage it is found that such interfaces not only considerably speed up the spreading but also cause the enhancement of the damaged area of the sample these statements are based on the evaluation of relevant exponents which characterize the spatio temporal spreading of the damage

low lying excitations in the square triangle random tiling model we consider the sub dominant eigenstates of the transfer matrix for the square triangle random tiling model on an infinite strip of width l a numerical algorithm for generation of the corresponding solution of the bethe ansatz is developed numerical finite size scaling analysis of the associated eigenvalues reveals the presence of both integer and non integer critical exponents the analytical value of one of the non integer exponents is found it is also shown numerically that along with the leading correction to the free energy density for some excitations there is a term proportional to

finite size scaling in strips antiperiodic boundary conditions the exact values of the universal amplitude a relating the correlation length xi approximately l a to the strip width l at the critical point of ising and 3 state potts models are obtained for the case of antiperiodic or twisted boundary conditions predictions are also made for the finite size scaling behaviour of the interfacial tension

critical behaviour of the bond interacting self avoiding walk the phase diagram for the bond interacting self avoiding walk is calculated using transfer matrices on finite strips the model is shown to have a richer phase diagram than the related point model in addition to the standard collapse transition we find a line of high order phase transitions which we conjecture to be in the berezinskii kosterlitz thouless bkt universality class terminating in a critical end point

bulk and surface critical behavior of the three dimensional ising model and conformal invariance using a continuous cluster monte carlo algorithm we investigate the critical three dimensional ising model in its anisotropic limit from the ratio of the magnetic correlations in the strong and the weak coupling directions we determine the length ratio relating the isotropic ising model and the anisotropic limit on this basis we simulate the critical ising model on a spherocylinder s2 x r1 i e a curved geometry obtained from a conformal mapping of the infinite space r3 from correlation lengths along the spherocylinder combined with the prediction of conformal invariance we estimate the magnetic and thermal scaling dimensions as x h 0 5182 6 and x t 1 419 7 respectively the behavior of the binder cumulant is also determined in the limit of an infinitely long spherocylinder next free boundary conditions are imposed on the equators of the spherocylinder and thus the geometry s1 x s x r1 is obtained the surface magnetic scaling dimension is estimated as x s h 1 263 5 the consistency of the aforementioned estimations and existing results confirms that the three dimensional ising model is conformally invariant further the precision of these results reveals that as in two dimensions conformal mappings provide a powerful tool to investigate critical phenomena with the continuous cluster algorithm we also perform simulations of systems inside a conventional solid cylinder the surface magnetic correlation length differs within the estimated error margin by a factor pi 2 from that along a half spherocylinder s1 x s x r1 with the same radius

nonuniversal critical behaviour in planar ising models with extended radially symmetric defects using conformal mapping and finite size scaling the authors determine the local magnetic exponent near a defect characterized by couplings of the form j r j 1 a r in accordance with phenomenological considerations they find that it depends continuously on the amplitude a both for a defect in the interior and on the boundary

the ashkin teller quantum chain and conformal invariance the authors study the finite size effects for the fourth state one dimensional quantum chain introduced by kohmoto et al 1981 using different boundary conditions from the corrections to the ground state energy for periodic boundary conditions they verify that the central charge of the virasoro algebra is equal to one in the whole domain of criticality their numerical study suggests a new relation between the corrections to the ground state energy with free boundary conditions and with periodic boundary conditions various critical exponents including the surface ones and those corresponding to the para fermions are determined

finite size scaling for directed bond percolation with and without cycles on a triangular lattice the authors apply finite size scaling and phenomenological renormalisation group arguments to the problems of directed acyclic directed cyclic and undirected bond percolation on a triangular lattice the results are in good agreement with known estimates and show that the phenomenological renormalisation procedure is sensitive to the difference between global and local directional biases as well as the distinction between locally directed and fully isotropic problems in addition the authors draw tentative comments on the extension to directed problems of the relation a pi eta where a is the inverse correlation length amplitude of a strip of finite width at criticality and eta is the exponent that describes the decay of correlations at the critical point known to hold for various isotropic systems

star triangle approach to boundary behavior in the two dimensional ising model abstract hilhorst and van leeuwen showed how to calculate boundary properties of the ising model on the triangular lattice by iterating a mapping based on the star triangle transformation we apply this approach to the ising model with homogeneous initial couplings in both the semi infinite and strip geometries several exact results for the boundary correlation length and the magnetization are reproduced the correlation dimensionality transition for enhanced edge couplings dual of abraham s interface unbinding transition is also considered

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

multicriticality in a self dual potts model the authors explore the self dual plane of a two dimensional potts model with vacancies and four spin interactions using finite size scaling of transfer matrix results since the transfer matrix construction is based on the random cluster representation of the potts model its application is not restricted to an integer number q of potts states for q or 4 the self dual plane contains a critical region belonging to the ordinary potts universality class and a region of first order transition points the two regions are separated by a line of which a range consists of potts tricritical points while another range is of a first order nature the point separating these two ranges is for 0 q or 9 4 identified with the multicritical point of which an exact solution has recently been given by nienhuis et al 1979

critical exponents near a random fractal boundary the critical behaviour of correlation functions near a boundary is modified from that in the bulk when the boundary is smooth this is known to be characterized by the surface scaling dimension we consider the case when the boundary is a random fractal specifically a self avoiding walk or the frontier of a brownian walk in two dimensions and show that the boundary scaling behaviour of the correlation function is characterized by a set of multifractal boundary exponents given exactly by conformal invariance arguments to be this result may be interpreted in terms of a scale dependent distribution of opening angles of the fractal boundary on short distance scales these are sharply peaked around similar arguments give the multifractal exponents for the case of coupling to a quenched random bulk geometry

finite size effects on the critical structure factor of the two dimensional ising model explicit calculations of the critical structure factor of the planar ising model on square lattices with a variety of boundaries are compared with the results of conformal invariance monte carlo methods are used for square circular and 2 1 rectangular geometries with free boundary conditions transfer matrices are used for an infinite strip with periodic boundary conditions good agreement is found for wavevectors less than a quarter of a reciprocal lattice spacing

finite size scaling for correlations of quantum spin chains at criticality we study the finite size scaling behavior of two point correlation functions of translationally invariant many body systems at criticality we propose an efficient method for calculating the two point correlation functions in the thermodynamic limit from numerical data of finite systems our method is most effective when applied to a two dimensional classical system which possesses a conformal invariance by using this method with numerical data obtained from exact diagonalizations and monte carlo simulations we study the spin spin correlations of the quantum spin 1 2 and 3 2 antifierromagnetic chains in particular the logarithmic corrections to power law decay of the correlation of the spin 1 2 isotropic heisenberg antiferromagnetic chain are studied thoroughly we clarify the cause of the discrepancy in previous calculations for the logarithmic corrections our result strongly supports the field theoretic prediction based on the mappings to the wess zumino witten nonlinear model or the sine gordon model we also treat logarithmic corrections and crossover phenomena in the spin spin correlation of the spin 3 2 isotropic heisenberg antiferromagnetic chain our results are consistent with the affleck haldane prediction that the correlation of the spin 3 2 chain exhibits a crossover to the same asymptotic behavior as in the spin 1 2 chain

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

a fast algorithm for linear estimation of two dimensional isotropic random fields the problem considered involves estimating a two dimensional isotropic random field given noisy observations of this field over a disk of finite radius by expanding the field and observations in fourier series and exploiting the covariance structure of the resulting fourier coefficient processes recursions are obtained for efficiently constructing the linear least squares estimate of the field as the radius of the observation disk increases these recursions are similar to the levinson equations of one dimensional linear prediction in the spectral domain they take the form of schrodinger equations which are used to give an inverse spectral interpretation of our estimation procedure

finite size scaling and the two dimensional xy model shows that the finite size scaling assumption and particularly a conjectured relation involving the exponent eta are valid in the low temperature phase of the 2d xy model order by order in a perturbative expansion of the two point correlation function

finite size effects at 2d ising critical points via conformal mapping using recent results by cardy 1984 based on conformal invariance of critical correlation functions the authors calculate universal results for scattering functions s k susceptibilities correlation lengths and specific heat correction terms for finite ising systems in two dimensions with circular elliptical and rectangular shapes and free boundary conditions results show the effects of critical order on these quantities for a circle s k decays as 1 k2 eta for a large range of intermediate k values with an apparent exponent eta 0 09 the probable influence of end edge and domain wall effects in the rectangular geometry is discussed application of the results to experimental systems and other theoretical models is discussed

operator dimensions and surface exponents for the non linear schrodinger model at t 0 using the euler maclaurin formula the authors compute finite size corrections to the ground and excited state energies and momenta this enables them to obtain all possible operator scaling dimensions at the critical point t 0 and surface exponents for a variety of boundary conditions they extend the predictions of conformal invariance to include green functions with oscillating terms

two dimensional o n model in a staggered field nienhuis truncated o n model gives rise to a model of self avoiding loops on the hexagonal lattice each loop having a fugacity of n we study such loops subjected to a particular kind of staggered field w which for n has the geometrical effect of breaking the three phase coexistence linked to the three colourability of the lattice faces we show that at t 0 for w 1 the model flows to the ferromagnetic potts model with q n2 states with an associated fragmentation of the target space of the coulomb gas for t 0 there is a competition between t and w which gives rise to multicritical versions of the dense and dilute loop universality classes via an exact mapping and numerical results we establish that the latter two critical branches coincide with those found earlier in the o n model on the triangular lattice using transfer matrix studies we have found the renormalization group flows in the full phase diagram in the t w plane with fixed n superposing three copies of such hexagonal lattice loop models with staggered fields produces a variety of one or three species fully packed loop models on the triangular lattice with certain geometrical constraints possessing integer central charges 0 c 6 in particular we show that benjamini and schramm s rgb loops have fractal dimension df 3 2

logarithmic corrections in the two dimensional ising model in a random surface field in the two dimensional ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point we study this question by extensive monte carlo simulations for various strengths of disorder the calculated effective temperature or size dependent critical exponents fit with the field theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system s critical behaviour

marginally inhomogeneous semiinfinite two dimensional ising models the scaling dimensions of the semiinfinite two dimensional ising model with smoothly inhomogeneous couplings are determined in general by the eigenvalues of a schrodinger type equation the author obtains exact results for a marginal two parameter inhomogeneity that corresponds to a supersymmetric quantum mechanical potential the results are compared with predictions of conformal invariance

amplitude exponent relation for the correlation length in the 2 1 dimensional ising model for the critical 2 1 d ising model defined on a square lattice with antiperiodic boundary conditions numerical studies suggest relations among the critical exponents and the finite size scaling amplitudes of correlation lengths similar to those obtained in 1 1 dimensions from conformal invariance

study of polymers with crossing bonds on the square lattice using the transfer matrix technique finite size scaling phenomenological renormalization group and conformal invariance ideas we studied the model of polymers with crossing bonds on the square lattice we define an activity for bonds and an activity for a crossing of two bonds where is the interaction energy between the two bonds we calculated the correlation length for two strips of widths l and and we found the fixed points of the phenomenological renormalization group equations within this formalism we obtained the phase diagram for this model which shows three phases two of them being polymerized the estimated values of the exponents and along the transition between the non polymerized phase and regular polymerized phase are consistent with and believed to be exact for y 0

the effect of attractive monomer monomer interactions on adsorption of a polymer chain the authors have used transfer matrix techniques to study a model of polymer adsorption and collapse they consider the conventional model of a self avoiding walk with attractive nearest neighbour interactions on the square lattice and introduce adsorbing boundaries the numerical results are consistent with the existence of a multicritical point where the adsorption and collapse transitions coincide and suggest that the adsorption transition of a collapsed polymer chain in first order there is also clear evidence that the collapse transition lowers the adsorption temperature estimates of the surface scaling dimensions at the ordinary theta transition support the conjecture of seno and stella 1988 that the surface critical behaviour at the theta and theta points belong to different universality classes

conformal off diagonal boundary density profiles on a semi infinite strip the off diagonal profile odb v associated with a local operator v order parameter or energy density close to the boundary of a semi infinite strip with width l is obtained at criticality using conformal methods it involves the surface exponent xs and displays a simple universal behaviour which crosses over from surface finite size scaling when v l is held constant to corner finite size scaling when v l 0

marginal extended perturbations in two dimensions and gap exponent relations the most general form of a marginal extended perturbation in a two dimensional system is deduced from scaling considerations it includes as particular cases extended perturbations decaying either from a surface a line or a point for which exact results have been previously obtained the first order corrections to the local exponents which are functions of the amplitude of the defect are deduced from a perturbation expansion of the two point correlation functions assuming covariance under conformal transformation the perturbed system is mapped onto a cylinder working in the hamiltonian limit the first order corrections to the lowest gaps are calculated for the ising model the results confirm the validity of the gap exponent relations for the perturbed system

random trimer tilings we study tilings of the square lattice by linear trimers for a cylinder of circumference m we construct a conserved functional of the base of the tilings and use this to block diagonalize the transfer matrix the number of blocks increases exponentially with m the dimension of the block corresponding to the largest eigenvalue is shown to grow as 32 13 m we numerically diagonalize this block for m or 27 obtaining the estimate s infinity 0 158520 0 000015 for the entropy per site in the thermodynamic limit we present numerical evidence that the continuum limit of the model has conformal invariance we measure several scaling dimensions including those corresponding to defects of monomers and l shaped trimers the trimer tilings of a plane admits a two dimensional height representation monte carlo simulations of the height variables show that the height height correlations grows logarithmically at large separation and the orientation orientation correlations decay as a power law

critical properties of s 1 2 antiferromagnetic xxz chain with next nearest neighbour interactions we investigate numerically the critical lines and the critical properties of the fluid dimer and the neel dimer transitions of the s 1 2 antiferromagnetic xxz chain with next nearest interactions and we confirm that the universality class of this model belongs to the quantum sine gordon model as is expected from the bosonization the method which we use in this paper to calculate the critical lines is free from the logarithmic corrections on the kosterlitz thouless k t type transition line which have made the k t critical point difficult to obtain by the use of this method it is possible to determine the k t critical line with high precision from small size data and to identify the universality class

collapse of two dimensional linear polymers we study the collapse transition of a two dimensional very long polymer the model we consider is a lattice model where the chain is represented by a self avoiding walk with nearest neighbor attraction by using the transfer matrix technique we calculate exactly the thermal and geometrical properties of the polymer on strips of finite width we then use finite size scaling to determine the values of the tricritical point exponentsv1 0 55 0 01vu 1 15 0 15 1 v1 1 80 0 05 we compare these results to the other values already proposed in the literature

critical properties of the spin 1 2 heisenberg chain with frustration and bond alternation we study the heisenberg chain with frustration and alternation which is expressed by both analytically and numerically we focus on the case where there is no marginal operator which brings about the logarithmic corrections in various quantities by using the bosonization method we calculate the energy gap the change in the ground state energy due to the alternation so called energy gain the spin correlation and the string correlation not only their exponents but also their amplitudes and compare them with the results of the numerical diagonalization for finite systems we point out the existence of the logarithmic correction in the energy gain despite the absence of the marginal operator taking into account this logarithmic correction we can obtain a reasonable hyperscaling relation between the critical exponents of the energy gap and an energy gain from the numerical data

universal order parameter profiles in confined critical systems with boundary fields the authors consider systems at the bulk critical temperature with an ordering field applied at the boundary for various boundary geometries universal expressions for the spatial dependence of the order parameter are obtained by conformal mapping of the known results for the half space analytical results for strip wedge and other two dimensional geometries and for systems with spherical boundaries in arbitrary dimension are given

semi infinite two dimensional ising model with marginally inhomogeneous couplings and conformal invariance the authors consider a semi infinite two dimensional ising model with nearest neighbour couplings that deviate from the bulk critical couplings by al 2 where l is the distance from the surface the surface critical exponents of this system are non universal under a conformal mapping onto a strip of width l the al 1 inhomogeneity transforms into a l pi sin pi l l 1 for the square lattice the spectrum of the transfer matrix in the strip geometry is calculated exactly in the extreme anisotropic limit the analytical results and numerical results for the triangular lattice are compared with predictions of conformal invariance

critical behaviour in parabolic geometries the authors study two dimensional systems with boundary curves described by power laws using conformal mappings they obtain the correlations at the bulk critical point three different classes of behaviour are found and explained by scaling arguments which also apply to higher dimensions for an ising system of parabolic shape the behaviour of the order at the tip is also found

finite size corrections for ground states of the xxz heisenberg chain the method of de vega and woynarovitch 1985 is used to calculate finite size corrections to the ground state energy in different sectors for the xxz heisenberg chain finite size scaling amplitudes and correction to scaling exponents in the critical region are derived using conformal invariance a scaling dimension x pi gamma 2 pi is extracted corresponding to the electric field operator in the 8 vertex model this confirms a conjecture of baxter and kelland 1974 finite size scaling properties near the kosterlitz thouless critical point delta 1 are discussed

the ising model with long range ferromagnetic interactions a variational method based on the nearest neighbour ising model is used to derive an expression for the low temperature correlation function in the ising model with long range ferromagnetic interactions also by expanding the correlation function directly the authors demonstrate that the characteristic power law behaviour at large distances is irrelevant in the critical region when above the marginal range of interaction

new results for exactly solvable critical rsos models and vertex models in two dimensions a method for analytically calculating critical properties of two dimensional exactly solvable models is presented it is based on the calculation of finite size corrections of the critical system and on predictions by conformal field theory it is applied to the restricted solid on solid models found by andrews baxter and forrester the analysis of the eigenvalues of the finite size transfer matrices is performed using special functional equations of inversion identity type the results are given in terms of rogers dilogarithms an outlook is given on related problems e g the application to vertex models and the calculation of free energy and correlation lengths of integrable quantum chains at finite temperature

numerical study of conformal invariance in rsos models the author studies conformal invariance in the rsos models of andrews et al 1985 at both the ferromagnetic and antiferromagnetic transitions using finite size scaling of the transfer matrix the author confirms the conjecture of huse 1984 concerning the conformal classification of the ferromagnetic transitions and gives evidence that the antiferromagnetic transitions lie in the universality class of zn models in addition he shows that conformal results can be applied to anisotropic systems if logarithmic corrections are taken into account

universal amplitudes in finite size scaling generalisation to arbitrary dimensionality the relationship between the correlation length and critical exponents in finite width strips in two dimensions is generalised to cylindrical geometries of arbitrary dimensionality d for d not 2 these correspond however to curved spaces the result is verified for the spherical model

conformal invariance and the ising model on a spheroid we formulate conformal mappings between an infinite plane and a spheroid and one between a semi infinite plane and a half spheroid special cases of the spheroid include the surface of an infinitely long cylinder of a sphere and of a flat disc these mappings are applied to the critical ising model for the case of the sphere and the flat disc we derive analytical expressions for the second and the fourth moments of the magnetization density and thus for the binder cumulant next we investigate ising models on spheroids and half spheroids by means of a continuous cluster monte carlo method for simulations in curved geometries fixed and free boundary conditions are imposed for half spheroids the monte carlo data are analyzed by finite size scaling critical values of the binder cumulants and other ratios on the sphere and on the flat disc agree precisely with the exact calculations mentioned above at criticality we also sample two and one point correlation functions on spheroids on half spheroids respectively the magnetic and temperature scaling dimensions as determined from the monte carlo data and the theory of conformal invariance are in good agreement with exact results

conformal theory of a next nearest neighbour interaction model abstract a one dimensional quantum model with generalized next nearest neighbour interaction is studied and its conformal field theory is constructed the numerical results convince us of the existence of a critical phenomenon in this model the critical point condition and the value of the central charge c are given also the anomalous scaling dimensions of the conformal field are given

finite size scaling of the free energy levels in the ising and potts q 3 universality the finite size scaling of the free energy levels of privman and fisher 1984 is tested numerically on two dimensional lattice strips in the ising and q 3 potts universality the universal amplitudes and the free energy per site are obtained

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

current correlations in the nonlinear schrodinger model from conformal field theory the authors analyse the nonlinear schrodinger model the one dimensional bose gas by means of conformal field theory in conjunction with a newly developed cutoff procedure this makes it possible to obtain exact expressions for current correlators in the model a number of new results are presented including the expression for the two point current correlator on a finite size strip and the general n point current correlator on the plane all these results have the full time dependence and are presented to order 1 g where g is the strength of the repulsive delta function interaction

non analytic finite size corrections for the heisenberg chain in a magnetic field with free and twisted boundary conditions the finite size energy spectrum of the anisotropic heisenberg chain in an external magnetic field is calculated for free and twisted boundary conditions as with periodic boundary conditions it is found that the spectra exhibit non analytical terms which do not fit into the form predicted on the basis of conformal invariance unless extra commensurability conditions between the size of the system and the external field are introduced taking these conditions into account some scaling dimensions for associated models are derived

duality of ordinary and extraordinary surface critical behaviour in the two dimensional potts model the dual relationship between semi infinite two dimensional q state potts models with free and fixed spin boundary conditions is used to study the surface critical behaviour at the bulk critical temperature with fixed boundary spins i e the extraordinary transition both the magnetisation and energy densities have singularities of the same form mod t tc mod 2 alpha as the bulk free energy at t tc both the spin spin and energy energy correlations decay as r 4 parallel to the surface

numerical extension of cft amplitude universality to three dimensional systems conformal eld theory cft predicts universal relations between scaling amplitudes and scaling dimensions for two dimensional systems on innite length cylinders which hold true even independent of the model under consideration we discuss dierent possible generalizations of such laws to three dimensional geometries using a cluster update monte carlo algorithm we investigate the nite size scaling fss of the correlation lengths of several representatives of the class of three dimensional classical o n spin models we nd that choosing appropriate boundary conditions the two dimensional situation can be restored c 2000 elsevier science b v all rights reserved

finite size scaling and conformal invariance in a self dual quantum z 5 model considers the critical behaviour of a particular set of onedimensional self dual models with z n symmetry n or 5 the critical indices are evaluated using standard finite size scaling and by exploiting their relations with the mass gap amplitudes predicted by conformal invariance the results strongly suggest that the recently introduced z n quantum field theory is the underlying field theory for these statistical mechanics models

the critical behaviour of self dual z n spin systems finite size scaling and conformal invariance this paper is concerned with the critical properties of a family of self dual two dimensional z n models whose bulk free energy is exactly known at the self dual point the author s analysis is performed by studying the finite size behaviour of the corresponding one dimensional quantum hamiltonians which also possess an exact solution at their self dual point by exploring finite size scaling ideas and the conformal invariance of the critical infinite system the author calculates for n up to 8 the critical temperature and critical exponents as well as the central charge associated with the underlying conformal algebra the results strongly suggest that the z n quantum field theory of zamolodchikov and fateev is the underlying field theory associated with these statistical mechanical systems the author also tests for the z 5 case the conjecture that these models correspond to the bifurcation points in the phase diagram of the general z n spin model where a massless phase originates

a finite lattice study of the critical behaviour of the two dimensional biaxial next nearest neighbour ising model the critical behaviour of an ising model with competing first and third nearest neighbour interactions biaxial next nearest neighbour ising or bnnni model on the square lattice is investigated by finite lattice methods in the ferromagnetic region the phase boundary is located with an accuracy at least equal to that of alternative methods in the antiphase region distinctive structure in finite lattice estimators is found over an extended temperature range however the nature of the transition remains unclear

amplitude exponent relation for the correlation length in the spherical model for the critical spherical model in d r 1 dimensions finite size calculations of the spin spin and energy energy correlation lengths suggest relations among the critical exponents and the finite size scaling amplitudes of the correlation lengths similar to those obtained in 1 1 dimensions from conformal invariance for antiperiodic boundary conditions the results agree with numerical studies in the 2 1 dimensional ising model

symmetric extension methods for m channel linear phase perfect reconstruction filter banks the symmetric extension method has been shown to he an efficient way for subband processing of finite length sequences this paper presents an extension of this method to general linear phase perfect reconstruction filter banks we derive constraints on the length and symmetry polarity of the permissible filter banks and propose a new design algorithm in the algorithm different symmetric sequences are formulated in a unified form based on the circular symmetry framework the length constraints in symmetrically extending the input sequence and windowing the subband sequences are investigated the effect of shifting the input sequence is included when the algorithm is applied to equal length filter banks we explicitly show that symmetric extension methods can always be constructed to replace the circular convolution approach

radial fredholm perturbation in the two dimensional ising model and gap exponent relation we consider concentric circular defects in the two dimensional ising model which are distributed according to a generalized fredholm sequence i e at exponentially increasing radii this type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation the critical exponent of the local magnetization is obtained through finite size scaling using a corner transfer matrix approach in the extreme anisotropic limit it varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial hilhorst van leeuwen model through a conformal mapping of the system onto a strip the gap exponent relation is shown to remain valid for such an aperiodic defect

the spin 1 heisenberg chain with uniaxial anisotropy and its classical counterpart abstract the spin 1 heisenberg chain with uniaxial anisotropy is related to a two dimensional roughening model with anisotropic next nearest neighbor interactions using this relation some peculiar features of the phase diagram of the quantum chain can be explained naturally and predictions for the critical exponents are also obtained which agree with previous finite size scaling studies of the quantum model a numerical transfer matrix calculation of the free energy of the roughening model on infinite strips of small width n 6 yields a critical behavior consistent with the one found for the t 0 properties of the quantum chain

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

nonanalytic correlation length in ising systems with one surface defect line abstract a two dimensional ising system with ferromagnetic coupling and one defect line at distance l from the surface is solved exactly using pfaffians the system shows a singularity in the surface correlation length at a temperature ts which is smaller than the transition temperature tc of the bulk numerical studies using the transfer matrix technique suggest that this singularity is also present in an ising system with two defect lines at distance l

test of finite size scaling predictions in three dimensions a constrained monomer dimer cmd model on decorated hypercubic lattices which is exactly solvable in any dimensionality d is studied the model is critical in the limit of maximal packing of the dimer configurations allowed by the constraint for d 2 it is equivalent to the rooted tree model on the square lattice considered by duplantier and david 1988 the validity of two finite size scaling predictions in higher dimensionalities is studied 1 the existence of logarithmic corrections in the free energy due to corners and ii the amplitude exponent relation for the pair correlation function the logarithmic finite size corrections are obtained for arbitrary d for boundary conditions which are periodic for d or 0 dimensions and free in the remaining d d dimensions dimer dimer correlation functions are studied at d 3 for a system finite in two dimensions and infinite in the third it is shown that the amplitude exponent relation for the cmd model holds for d 2 and breaks down for d 3

integrable versus non integrable spin chain impurity models recent renormalization group studies of impurities in spin 1 2 chains appear to be inconsistent with bethe ansatz results for a special integrable model we study this system in more detail around the integrable point in parameter space and argue that this integrable impurity model corresponds to a non generic multi critical point using previous results on impurities in half integer spin chains a consistent renormalization group flow and phase diagram is proposed

percolation of the site random cluster model by monte carlo method we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation to simulate the model on a square lattice we combine the color assignation and the swendsen wang methods to design a highly efficient cluster algorithm with a small critical slowing down phenomenon to verify whether or not it is consistent with the bond random cluster model we measure several quantities such as the wrapping probability re the percolating cluster density p and the magnetic susceptibility per site p as well as two exponents such as the thermal exponent yt and the fractal dimension yh of the percolating cluster we find that for different exponents of cluster weight q 1 5 2 2 5 3 3 5 and 4 the numerical estimation of the exponents yt and yh are consistent with the theoretical values the universalities of the site random cluster model and the bond random cluster model are completely identical for larger values of q we find obvious signatures of the first order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site our results are helpful for the understanding of the percolation of traditional statistical models

tests of hyperuniversality for self avoiding walks a universal combination of amplitudes for the end to end distance of n step self avoiding walks and for the number of n step self avoiding polygons is estimated numerically for various lattices in d 2 universality of this amplitude combination is confirmed to good accuracy while in d 3 the data are consistent with universality but the error limits are rather large for finite width square lattice strips the authors calculate universal critical point correlation amplitudes by fixed fugacity monte carlo simulations in addition these amplitudes are calculated analytically either exactly or approximately by cardy s conformal mapping approach numerical values agree well with the theoretical predictions

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 critical amplitude relation for one dimensional quantum transitions and determination of the exponent eta a new critical amplitude relation which holds for one dimensional quantum ground state transitions is presented the relation yields an estimate of the sound velocity which appears in the conformal field theory as an a priori unknown parameter with the use of this relation the exponent eta can be explicitly determined from only the scaling fit of the off critical energy gap the relation is confirmed in the transverse ising model the s 1 2 anisotropic xy model and the three state potts model

potts and percolation models on bowtie lattices we give the exact critical frontier of the potts model on bowtie lattices for the case of q 1 the critical frontier yields the thresholds of bond percolation on these lattices which are exactly consistent with the results given by ziff et al j phys a 39 15083 2006 for the q 2 potts model on a bowtie a lattice the critical point is in agreement with that of the ising model on this lattice which has been exactly solved furthermore we do extensive monte carlo simulations of the potts model on a bowtie a lattice with noninteger q our numerical results which are accurate up to seven significant digits are consistent with the theoretical predictions we also simulate the site percolation on a bowtie a lattice and the threshold is s c 0 5479148 7 in the simulations of bond percolation and site percolation we find that the shape dependent properties of the percolation model on a bowtie a lattice are somewhat different from those of an isotropic lattice which may be caused by the anisotropy of the lattice

the number of incipient spanning clusters in two dimensional percolation using methods of conformal field theory we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k i n the limit when k is large the study of the structure of large clusters at the percolation threshold continues to pose interesting problems whose solution sheds light on the nature of the critical state in general recently some attention has been paid to incipient spanning clusters iscs these are clusters which connect two disjoint segments of the boundary of a macroscopically large region langlands et al 1 conjectured that the probability that at least one such cluster exists that is that the segments are connected is invariant under conformal transformations this statement was placed in the context of conformal field theory in 2 where an explicit formula was given for this crossing probability for a review of the status of conformal invariance in critical percolation see 3 more recently aizenman 4 has considered among other things the probability that there exist n distinct iscs connecting the two segmentsy in the case of a rectangular region 0 kl 0 l he has proved that the probability p n k l that the strip is traversed in the direction of length kl b y nindependent clusters satisfies the bounds a e n 2 k

finite size scaling of the quantum ising chain with periodic free and antiperiodic boundary conditions the authors give exact results for the energy spectrum of a chain of n ising spins in a transverse field with periodic free and antiperiodic boundary conditions the dependence of the energy gaps on boundary conditions is compatible with predictions of conformal invariance for correlation lengths in two dimensional strips the feasibility of calculating surface critical indices using phenomenological renormalisation with free boundary conditions and the convergence for large n are discussed