conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

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

correlation length in ising strips with free and fixed boundary conditions the correlation length of boundary spins in the ising model defined on strips of triangular lattice with free boundary conditions is determined with an efficient numerical procedure based on the star triangle transformation in the case of isotropic critical interactions the extrapolated amplitude of the correlation length is in excellent agreement with the value 2 pi eta sub predicted by conformal invariance an analytical formula for the amplitude in strips with anisotropic interactions is proposed fixing the spins on one edge reduces the amplitude of the correlation length on the other edge by a factor 1 2 the convergence of phenomenological renormalisation with free boundary conditions is studied

origin of the singular bethe ansatz solutions for the heisenberg xxz spin chain we investigate symmetry properties of the bethe ansatz wave functions for the heisenberg xxz spin chain the xxz hamiltonian commutes simultaneously with the shift operator t and the lattice inversion operator v in the space of 1 with the eigenvalue of t we show that the bethe ansatz solutions with normalizable wave functions cannot be the eigenstates of t and v with quantum number 1 1 where is the eigenvalue of v therefore the bethe ansatz wave functions should be singular for nondegenerate eigenstates of the hamiltonian with quantum number 1 1 it is also shown that such states exist in any nontrivial down spin number sector and that the number of them diverges exponentially with the chain length c 2000 published by elsevier science b v all rights reserved

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

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

accurate determination of the critical line of the square ising antiferromagnet in a field several points on the critical line of the simple quadratic antiferromagnetic ising model in a field are located with high precision this is accomplished by means of finite size scaling of the magnetic correlation length of n infinity strips the latter quantities were determined by means of the transfer matrix method for strip widths up to n 20 an expression possibly with the exact form is constructed which reproduces the critical line with an accuracy to the order of 10 10

finite size effects and infrared asymptotics of the correlation functions in two dimensions the finite size corrections approach to the calculation of the asymptotics of correlation functions containing the oscillating terms in the asymptotics in 1 1 dimensional theories is presented explicit formulae for the critical exponents in integrable models are obtained

solving the discrete l p approximation problem by a method of centers abstract the discrete lp approximation problem is a basic problem in approximation theory and optimization this problem is normally solved by newton type methods which are complicated by the nondifferentiability of the gradient function for p 1 2 this paper discusses a scheme and its implementation for solving this problem by a method of analytic centers which provides a unified treatment for all p 1 and has a polynomial bound of complexity the original problem is reformulated as a constrained convex programming problem which admits a self concordant logarithmic barrier a special structure of the newton system derived from minimizing the potential function is utilized to reduce the amount of computation some other implementation techniques are also presented computational results show that the method of centers is robust for all p

corrections to scaling and self duality in the restricted solid on solid model the corrections to scaling at and above the roughening transition tr in the restricted solid on solid model are studied by means of finite size scaling for semi infinite strips of width 2 to 10 it is shown that at a temperature tsd not far above the roughening temperature where the restricted solid on solid model is invariant under the duality transformation of the five state clock model the fugacity of the sine gordon operator must vanish for the dual truncated planar model this means that the core energy of the vortices diverges between ts and tr the corrections to scaling do not reach their asymptotic behaviour but are dominated by the contributions from the delta phi 4 operator associated with the restriction to steps of height one

on infeasibility of systems of convex analytic inequalities abstract in this paper we address the problem of the infeasibility of systems defined by convex analytic inequality constraints in particular we investigate properties of irreducible infeasible sets and provide an algorithm that identifies a set of all constraints k that may affect the feasibility status of the system after some perturbation of the right hand sides we analyze properties of the irreducible sets as well as infeasibility sets in connection with the set k showing in particular that every infeasible system contains an inconsistent subsystem of cardinality not greater than the number of variables plus one the results presented in this paper are generalizations of a theory developed for the systems of quadratic and linear inequality constraints

an interior point algorithm of o m ln e iterations for c 1 convex programming we present a theoretical result on a path following algorithm for convex programs the algorithm employs a nonsmooth newton subroutine it starts from a near center of a restricted constraint set performs a partial nonsmooth newton step in each iteration and converges to a point whose cost is within accuracy of the optimal cost in o sqrt m left ln varepsilon right iterations wherem is the number of constraints in the problem unlike other interior point methods the analyzed algorithm only requires a first order lipschitzian condition and a generalized hessian similarity condition on the objective and constraint functions therefore our result indicates the theoretical feasibility of applying interior point methods to certainc1 optimization problems instead ofc2 problems since the complexity bound is unchanged compared with similar algorithms forc2 convex programming the result shows that the smoothness of functions may not be a factor affecting the complexity of interior point methods

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

a transfer matrix monte carlo study of random penrose tilings the authors investigate the entropic properties of a simple two dimensional random quasicrystal model a random tiling by the 36 and 72 rhombi applying the transfer matrix monte carlo tmmc method to random tilings for the first time they have calculated the entropy as a function of phason strain they confirm earlier results that the state of zero phason strain i e ten fold symmetry has the largest entropy the entropy is 0 4810 5 per tile in addition by fitting the dependence of the entropy on the phason strain they determined the three stiffness constants in the phason elasticity one of which is not measurable by previous approaches they compare the efficacy of the tmmc method with that of other methods

hunting for the central charge of the virasoro algebra six and eight state spin models in two dimensions conformal invariance has important implications for the finite size scaling properties of the spectra of transfer matrices and quantum chains at the critical point some relations between the finite size scaling amplitudes are obtained which can be used as a test of conformal invariance and implicitly to distinguished between second order and first order phase transitions the numerical values of the scaling amplitudes give the scale dimensions of various operators six and eight state self dual quantum chains with cubic symmetries are considered at the critical point for three values of the coupling constant the systems are found to be conformal invariant and estimates for several critical exponents are obtained based on the approximate values of the critical exponent one tries to find the values of the corresponding central charges of the virasoro algebras

finite size studies of the ashkin teller model the authors study the ashkin teller model in the time continuous hamiltonian version finite size scaling is used to calculate the magnetic gamma m electric gamma p and thermal alpha and nu critical exponents for several values of the coupling constant lambda the results confirm the believed extended scaling relations and suggest a conjecture relating the mass gap amplitudes and critical indices in the hamiltonian context

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

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

spatial anisotropy and rotational invariance of critical hard squares we develop a new method to analyse solvable models defined on a square lattice rotated through an arbitrary angle phi with respect to the coordinate axes in the method we introduce auxiliary faces into a rotated system to relate it with an inhomogeneous one in the natural orientation phi 0 the inhomogeneous system is investigated by commuting a transfer matrix argument as an application of the method we consider interacting hard squares at the critical point we discuss relations between spatial anisotropy and rotational or conformal invariance of the model in calculations of finite size properties

boundary susceptibility in the open xxz chain in the first part we calculate the boundary susceptibility b in the open xxz chain at zero temperature and arbitrary magnetic field h by the bethe ansatz we present analytical results for the leading terms when h where is a known scale and a numerical solution for the entire range of fields in the second part we calculate susceptibility profiles near the boundary at finite temperature t numerically by using the density matrix renormalization group for transfer matrices and analytically for t 1 by field theoretical methods finally we compare b at finite temperature with a low temperature asymptotics which we obtain by combining our bethe ansatz result with recent predictions from bosonization

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

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

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

universal functions in finite size scaling a numerical study in the ising and potts q 3 universality class the universality of the correlation length order parameter and susceptibility amplitudes is studied in the vicinity of the critical point of two dimensional models on strips with periodic boundary conditions for the ising and potts q 3 universality class the results confirm privman fisher conjecture 1984

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

phase diagram of a random tiling quasicrystal we study the phase diagram of a two dimensional random tiling model for quasicrystals at proper concentrations the model has 8 fold rotational symmetry landau theory correctly gives most of the qualitative features of the phase diagram which is in turn studied in detail numerically using a transfer matrix approach we find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first order or continuous transitions exact solutions are given in all phases except for the quasicrystal phase and for the phase boundaries between them we calculate numerically the phason elastic constants and entropy density and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8 fold rotational symmetry in addition to the obvious application to quasicrystals this study generalizes certain surface roughening models to two dimensional surfaces in four dimensions

operator content of the xxz chain the finite size scaling spectra of the xxz heisenberg chain are presented for even and odd numbers of sites respectively the operator content is given for free as well as for toroidal boundary conditions

conformal dimensions in bethe ansatz solvable models models solvable by the hierarchy of bethe ansatze i e by the multicomponent bethe ansatz are considered the spectrum of conformal dimensions which determines the long distance asymptotics of correlations is calculated this asymptotics in a general case is described by the direct sum of conformal theories each possessing a central charge equal to one

operator content of the blume capel quantum chain the authors calculated the conformal anomaly number of the blume capel quantum chain via finite size corrections to the ground state energy in addition they compute at the tricritical point the lowest excitations of the spectrum to be compared with the theoretical description in terms of the irreducible representations of the corresponding virasoro algebra

non erasing chomsky schutzenberger theorem with grammar independent alphabet abstract the famous theorem by chomsky and schutzenberger cst says that every context free language l over an alphabet is representable as h d r where d is a dyck language over a set of brackets r is a local language and h is an alphabetic homomorphism that erases unboundedly many symbols berstel found that the number of erasures can be linearly limited if the grammar is in greibach normal form berstel and boasson and later independently okhotin proved a non erasing variant of cst for grammars in double greibach normal form in all these cst statements however the size of the dyck alphabet depends on the grammar size for l in the stanley variant of the cst only depends on and not on the grammar but the homomorphism erases many more symbols than in the other versions of cst also the regular language r is strictly locally testable but not local we prove a new version of cst which combines both features of being non erasing and of using a grammar independent alphabet in our construction is polynomial in namely o 46 and the regular language r is strictly locally testable using a recent generalization of medvedev s homomorphic characterization of regular languages we prove that the degree in the polynomial dependence of on may be reduced to just 2 in the case of linear grammars in double greibach normal form

equality of directional critical exponents in multiparameter percolation models in multiparameter percolation models a directional critical exponent may be considered for each direction of approach in the parameter space to a point on the critical surface an elementary coupling argument shows that for each point on the critical surface the directional critical exponents are equal for all directions strictly in the positive orthant using the substitution method the set of directions with equal directional critical exponents can he extended beyond the orthant the anisotropic triangular lattice bond percolation model is used to illustrate the method

logarithmic corrections to finite size scaling in strips abstract the corrections to the finite size scaling behaviour of the eigenvalues of the transfer matrix of a critical theory defined on an infinitely long strip of finite width which occur when the hamiltonian contains a marginal operator are computed using conformal invariance they show a calculable universal logarthmic character for the four state potts model they agree with numerical data

six vertex model with rotated boundary conditions we investigate the six vertex model on a square lattice rotated through an arbitrary angle with respect to the coordinate axes a model recently introduced by litvin and priezzhev auxiliary vertices are used to define an inhomogeneous system which leads to a one parameter family of commuting transfer matrices a product of commuting transfer matrices can be interpreted as a transfer matrix acting on zigzag walls in the rotated system using an equation for commuting transfer matrices we calculate their eigenvalues finite size properties of the model are discussed from the viewpoint of the conformal field theory

a new approach to the calculation of the central charge the author shows that the central charge c of the virasoro algebra is determined by the spectrum of the hamiltonian l0 nl0 corresponding to a partition function which is invariant under the subgroup of modular transformations generated by s using this result he discusses in detail a new possibility of determining c for a given system at criticality which turns out to give excellent estimates even if the lattices accessible to numerical calculation are very small this enables him to predict the central charge of some spin systems furthermore his approach to the determination of c leads to new universal functions interpolating between criticality and off criticality

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

a primal dual potential reduction method for problems involving matrix inequalities we describe a potential reduction method for convex optimization problems involving matrix inequalities the method is based on the theory developed by nesterov and nemirovsky and generalizes gonzaga and todd s method for linear programming a worst case analysis shows that the number of iterations grows as the square root of the problem size but in practice it appears to grow more slowly as in other interior point methods the overall computational effort is therefore dominated by the least squares system that taust be solved in each iteration a type of conjugate gradient algorithm can be used for this purpose which results in important savings for two reasons first it allows us to take advantage of the special structure the problems often have e g lyapunov or algebraic riccati inequalities second we show that the polynomial bound on the number ofiterations remains valid even if the conjugate gradient algorithm is not run until completion which in practice can greatly reduce the computational effort per iteration we describe in detail how the algorithm works for optimization problems with l lyapunov inequaliues each of size m we prove an overall worst case operation count of o mssll5 the average case complexity appears to be closer to o m4ll5 this estimate is justified by extensive numerical experimentation and is consistent with other researchers experience with the practical performance of interior point algorithms for linear programming this result means that the computational cost of extending current control theory based on the solution of lyapunov or riccati equations to a theory that is based on the solution of multiple coupled lyapunov or riccati inequalities is modest

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

logarithmic singularity in the surface free energy near commensurate incommensurate transitions the authors study finite size scaling behaviour of a two dimensional random tiling model this model exhibits commensurate incommensurate phase transitions of the pokrovsky talapov type where anisotropic scaling appears a simple scaling argument near this transition suggests an integral surface critical exponent which in turn implies a logarithmic singularity with a universal coefficient in the surface free energy they confirm the existence of this singularity numerically employing the transfer matrix method in the case of free boundary conditions

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

a combined homotopy interior point method for convex nonlinear programming abstract in this paper we present a new interior point method combined homotopy interior point method chip method for convex nonlinear programming without strict convexity of the logarithmic barrier function and boundedness and nonemptiness of the solution set we prove that for any 0 an solution of the problem can be obtained by the chip method to our knowledge strict convexity of the logarithmic barrier function and nonemptiness and boundedness of the solution set are the essential assumptions of the well known center path following method therefore the chip method essentially reduces the assumptions of the center path following method and can be applied to more general problems

a polynomial time algorithm for the local testability problem of deterministic finite automata the local testability problem of deterministic finite automata is investigated a locally testable language is a language with the property that for some nonnegative integer k whether or not a word w is in the language depends on 1 the prefix and suffix of w of length k and 2 the set of substrings of w length k 1 without regard to the order in which these substrings occur the local testability problem is given a deterministic finite automation to decide whether or not it accepts a locally testable language the authors present an o n sup 2 time algorithm for the local testability problem based on two simple properties that characterize locally testable automata

families of locally testable languages kim mcnaughton and mccloskey have produced a polynomial time algorithm in order to test if a deterministic automaton recognizes a locally testable language we provide a characterization in terms of automata for the strictly locally testable languages and for the strongly locally testable languages two subclasses of locally testable languages these two characterizations lead us to polynomial time algorithms for testing these families of languages

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

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

spectra of non hermitian quantum spin chains describing boundary induced phase transitions the spectrum of the non hermitian asymmetric xxz chain with additional non diagonal boundary terms is studied the lowest lying eigenvalues are determined numerically for the ferromagnetic chain the temporal correlation length shows the same properties as the spatial correlation length for the antiferromagnetic chain we find a conformal invariant spectrum where the partition function corresponds to the one of a coulomb gas with only magnetic charges this is in contrast to the case of diagonal boundary terms where one finds only electric charges similar results are obtained in a toy model that can be diagonalized analytically in terms of free fermions

corrections to finite size scaling for quantum chains the authors compute the leading order correction to the energy gap at the critical point for the anisotropic ising and the z3 potts quantum chains periodic anti periodic and free boundary conditions are considered for the ising case the corrections are independent of the boundary conditions in the z3 case the correction is the same for anti periodic and free boundary conditions but is 2 5 smaller for the periodic case the authors have no explanation for this phenomenon

minimal representation of convex regions defined by analytic functions in this paper we are concerned with characterizing minimal representation of feasible regions defined by both linear and convex analytic constraints we say that a representation is minimal if every other representation has either more analytic nonlinear constraints or has the same number of analytic constraints and at least as many linear constraints we prove necessary and sufficient conditions for the representation to be minimal these are expressed in terms of the redundant constraints pseudo analytic constraints and implicit equality constraints in order to prove the minimal representation theorem we present results on the facets of the convex regions defined by analytic constraints finally we outline the steps of the procedure that could be used to determine a minimal representation

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

the modified xxz heisenberg chain conformal invariance and the surface exponents of c 1 systems the authors present the operator content of the xxz chain in the presence of external fields the finite size scaling spectra can be expressed in terms of irreps of shifted u 1 kac moody algebras the shift depending on the external fields using an explicit feigin fuchs construction 1982 they project out from these spectra the operator content of c 1 systems with free fixed and mixed boundary conditions they also show how this projection mechanism works for a finite number of sites

magnetization at corners in two dimensional ising models we investigate the corner spin magnetization of two dimensional ferromagnetic ising models in various wedge geometries results are obtained for triangular and square lattices by numerical studies on finite wedges using the star triangle transformation as well as analytic calculations using corner transfer matrices and a fermionic representation of the row to row transfer matrix the corner magnetizations vanish at the bulk critical temperature tc with an exponent c differing from the bulk exponent for isotropic systems with free edges we find that c is given simply by c 2 where is the angle at the corner for apex magnetizations of conical lattices we obtain the strikingly similar result a 4 these formulas apply equally well to anisotropic lattices if the angle is interpreted as an effective angle eff determined by the relative strengths of the interactions

free energy amplitude in finite size scaling the baxter model the critical amplitude a0 of the free energy density of the baxter model is studied numerically on strips with widths l 2 12 as a function of the four spin interaction k4 it remains almost constant near to double the exactly known ising result a0 2a0ising pi 6 in the range of k4 values for which an extrapolation to infinite width is possible

on the symmetry of universal finite size scaling functions in anisotropic systems we postulate a symmetry of universal finite size scaling functions under a certain anisotropic scale transformation which connects the properties of a finite two dimensional 2d system at criticality with generalized aspect ratio 1 to a system with 1 the symmetry is formulated within a finite size scaling theory and expressions for several universal amplitude ratios are derived the predictions are confirmed within the exactly solvable weakly anisotropic 2d ising model and are checked within the strongly anisotropic 2d dipolar in plane ising model using monte carlo simulations

the spin 1 2xxz heisenberg chain the quantum algebra uq sl 2 and duality transformations for minimal models the finite size scaling spectra of the spin 1 2 xxz heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c 1 including the unitary and nonunitary minimal series taking into account the half integer angular momentum sectors which correspond to chains with an odd number of sites in many cases leads to new spinor operators appearing in the projected systems these new sectors in the xxz chain correspond to new types of frustration lines in the projected minimal models the corresponding new boundary conditions in the hamiltonian limit are investigated for the ising model and the 3 state potts model and are shown to be related to duality transformations which are an additional symmetry at their self dual critical point by different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite xxz chain the observed degeneracies in the energy and momentummore spectra are shown to be the consequence of intertwining relations involving u sub q sl 2 quantum algebra transformations 35 refs 3 tabs less

some finite size amplitudes and critical exponents for potts and ashkin teller quantum chains analytic expressions are derived for the leading finite size corrections to a class of energy eigenvalues of the potts and ashkin teller quantum chains making use of their equivalences with a modified xxz heisenberg chain assuming conformal invariance exact results are thence obtained for some bulk scaling dimensions and surface exponents in these models

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

excited states in the twisted xxz spin chain we compute the finite size spectrum for the spin chain with twisted boundary conditions for anisotropy in the regime and arbitrary twist the string hypothesis is employed for treating complex excitations the bethe ansatz equtions are solved within a coupled nonlinear integral equation approach with one equation for each type of string the root of unity quantum group invariant periodic chain reduces to the chain with a set of twist boundary conditions an integer multiple of for this model the restricted hilbert space corresponds to a unitary conformal field theory and we recover all primary states in the kac table in terms of states with specific twist and strings

logarithmic corrections to gap scaling in random bond ising strips numerical results for the first gap of the lyapunov spectrum of the self dual random bond ising model on strips are analysed it is shown that finite width corrections can be fitted very well by an inverse logarithmic form predicted to hold when the hamiltonian contains a marginal operator

codes circulaires automates locaux et entropie abstract the theory of codes and finite automata is applied to prove the existence of codes suitable for coding arbitrary sequences into a constrained system of sequences called system of finite type the techniques are different from those used by adler coppersmith hassner and marcus in earlier work on the same problem

random tilings with quasicrystal order transfer matrix approach the random tiling of the plane by a set of objects e g rhombi related by rotational e g tenfold symmetries is a paradigm for the formation of quasiperiodic order due to entropy such tilings are mapped to a higher dimensional space where they form hypersurfaces analogous to the interfaces in a solid on solid model the author argues that the fluctuations of the hypersurface should be described by a gradient squared free energy of entropic origin this implies quasi long range order in d 2 he shows how the random tiling can be decomposed into layers defines a transfer matrix and give prescriptions for using this method to determine numerically the stiffness of the gradient free energy

finite size effects in a non half filled hubbard chain the finite size effects in the spectrum of a hubbard chain are obtained for both the repulsive and attractive cases it is shown that the finite size corrections similar to the case of a heisenberg chain or bose gas are nonanalytic unless some conditions are imposed on the chemical potential magnetic field and chain length if these conditions are met the spectrum shows a similar tower structure as expected in conformal theories although the model in general is not conformally invariant in the special case when the two fermi velocities are equal the model is conformally invariant with c 2 the indices are similar to the gaussian form and there are four marginal operators

finite size scaling amplitudes in a random tiling model we study finite size corrections to the free energy in a two dimensional random tiling model this model is equivalent to an asymmetric six vertex model and exhibits commensurate incommensurate phase transitions of the pokrovsky talapov type we calculate finite size scaling amplitudes of the free energy inside the incommensurate phase analytically and numerically by employing a transfer matrix method both periodic and free boundary conditions are considered these amplitudes are consistent with predictions of the theory of conformal invariance with the conformal charge c 1

finite size effects in the integrable xxz heisenberg model with arbitrary spin the finite size effects in the spectrum of the integrable xxz heisenberg chain with arbitrary spin s are studied analytically on the basis of the string hypothesis for bound states and numerically by solving the associated bethe ansatz equations the finite size corrections to the spectrum and to the low temperature behaviour of the free energy are found to be similar to the universal predictions for conformally invariant theories although the model is in general not lorentz invariant since it can have an arbitrary number of branches for low energy excitations with different fermi velocities depending on the value of s and the anisotropy parameter gamma

critical behaviour of a model with nnn interaction a one dimensional quantum model with next nearest neighbour interaction is studied under the long wavelength approximation the authors predict that this model belongs to the same universality class as the ising model this conclusion is checked with a numerical solution which is consistent with the prediction in both critical point and critical exponent

universal ising dynamics in two dimensions we explore several dominant eigenvalues of the spectra of markov matrices governing the dynamics of models in the universality class of the two dimensional ising model by means of a variational approximation we determine autocorrelation times of progressively rapid relaxation modes the approximation of one eigenstate associated with the slowest mode is employed in a variance reducing monte carlo method the resulting correlation times for which statistical errors exceed the systematic errors associated with the variational approximation are used for a finite size scaling analysis which corroborates universality of the dynamic critical exponent z for three distinct ising models on the square lattice tentative variational results for subdominant states strongly suggest that the amplitudes of the divergent time scales associated with different relaxation modes differ solely by metric factors setting a single non universal time scale for each model a by product of our analysis is a highly accurate confirmation of static universality

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

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 corrections and numerical calculations for long spin 1 2 heisenberg chains in the critical region leading and next to leading order finite size corrections to the ground and first excited states are calculated for the spin 1 2 anisotropic heisenberg model in the critical region the analytic results are compared to numerical data obtained for chains up to a length of n 1024 it is found that near the isotropic point the asymptotic region where the results obtained for n to infinity are applicable sets in at very large n values and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms even at large n 100 chain lengths

line search termination criteria for collinear scaling algorithms for minimizing a class of convex functions many successful quasi newton methods for optimization are based on positive definite local quadratic approximations to the objective function that interpolate the values of the gradient at the current and new iterates line search termination criteria used in such quasi newton methods usually possess two important properties first they guarantee the existence of such a local quadratic approximation second under suitable conditions they allow one to prove that the limit of the component of the gradient in the normalized search direction is zero this is usually an intermediate result in proving convergence collinear scaling algorithms proposed initially by davidon in 1980 are natural extensions of quasi newton methods in the sense that they are based on normal conic local approximations that extend positive definite local quadratic approximations and that they interpolate values of both the gradient and the function at the current and new iterates line search termination criteria that guarantee the existence of such a normal conic local approximation which also allow one to prove that the component of the gradient in the normalized search direction tends to zero are not known in this paper we propose such line search termination criteria for an important special case where the function being minimized belongs to a certain class of convex functions

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

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

on the descriptional complexity of stateless deterministic ordered restarting automata abstract stateless deterministic ordered restarting automata accept exactly the regular languages here we study the descriptional complexity of these automata taking the size of the tape alphabet as the complexity measure we present a construction that turns a stateless deterministic ordered restarting automaton that works on an alphabet of size n into an equivalent nondeterministic finite state acceptor of size at most 2 o n and we prove that this bound is sharp with respect to its order of magnitude in addition we investigate the descriptional complexity of some operations for regular languages that are given through stateless deterministic ordered restarting automata based on these results we then show that many decision problems like emptiness finiteness and inclusion are pspace complete for these automata finally we propose three ways of associating relations to deterministic ordered restarting automata in the most general setting we obtain succinct representations for all rational relations in the most restricted setting we obtain exactly those rational functions that map the empty word to itself and by extending the stateless deterministic ordered restarting automaton into a transducer we obtain exactly all those transductions on words that are mso definable

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

a large step analytic center method for a class of smooth convex programming problems in this paper a large step analytic center method for smooth convex programming is proposed the method is a natural implementation of the classical method of centers it is assumed that the objective and constraint functions fulfil the so called relative lipschitz condition with lipschitz constant m 0 a great advantage of the method over the existing path following methods is that the steps can be made long by performing linesearches in this method linesearches are performed along the newton direction with respect to a strictly convex potential function when located far away from the central path when sufficiently close to this path a lower bound for the optimal value is updated it is proven that the number of iterations required by the algorithm to converge to an epsilon optimal solution is o 1 m 2 sqrt n ln epsilon or o 1 m 2 n ln epsilon depending on the updating scheme for the lower bound

critical exponents of two dimensional potts and bond percolation models critical exponents of the two dimensional q state potts model are calculated by means of finite size scaling and transfer matrix techniques for continuous q results for the temperature exponent agree accurately with the conjecture of den nijs 1979 the magnetic exponent is found to behave in accordance with the conjecture of nienhuis et al 1980

conformal invariance in incommensurate phases we study finite size corrections to the free energy of free fermion models on a torus with periodic twisted and fixed boundary conditions inside the critical striped incommensurate phase the free energy densityf n m on ann m square lattice with periodic or twisted boundary conditions scales asf n m f a s nm we derive exactly the finite size scaling fss amplitudesa s as a function of the aspect ratios m n these amplitudes are universal because they do not depend on details of the free fermion hamiltonian we establish an equivalence between the fss amplitudes of the free fermion model and the coulomb gas system with electric and magnetic defect lines the twist angle generates magnetic defect lines while electric defect lines are generated by competition between domain wall separation and system size the fss behavior of the free fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec l for instance the fss amplitude on an infinite cylinder with fixed boundary conditions is found to be one quarter of that with periodic boundary conditions finally we conjecture the exact form of the fss amplitudes for an interacting fermion model on a torus numerical calculations employing the bethe ansatz confirm our conjecture in the infinite cylinder limit

universal amplitude exponent relations for interfaces and conformal mappings the author considers the finite size fs scaling behaviour of the transverse correlation lengths xi sub n for an interface confined in a strip geometry exactly at a second order fluctuation dominated wetting transition he shows that the dimensionless amplitude ratios a sub n sigma l2 kbt xi sub n with sigma the surface stiffness coefficient are related to the short distance expansion critical exponent theta by a sub n pi 2n n theta 1 2 for all fluctuation dominated wetting transitions provided the binding potential v y in the capillary wave model is conformally mapped from the semi infinite plane he argues that the existence of this amplitude exponent relation reflects the conformal invariance of the capillary wave model lagrange density and lists a number of one point functions which can be shown to exhibit this invariance explicitly

quadratically constrained convex quadratic programmes faulty feasible regions abstract we are concerned with the problem of minimizing a convex quadratic function subject to convex quadratic constraints in particular we are concerned with the application of the method of analytic centres to problems having a faulty feasible region i e a region that is either unbounded or not full dimensional each iteration of a method of centres must determine an analytic centre of a truncated feasible region if the feasible region is faulty then the truncated region may have no interior it may have no analytic centre it may have an infinity of centres or it may have a unique centre thus the difficulty caused by faulty feasible regions is that even when the problem has a solution the method of centres may fail typically faulty regions have been dealt with by the direct method of adding more constraints and variables often involving a big m constant our method is unique in that it results in a reduction in the number of constraints and effectively in the number of variables

the non interacting hard square lattice gas ising universality the critical exponents of the non interacting hard square lattice gas model are determined by means of series analysis and finite size scaling the series analysis leads to results for the exponents that are consistent with the expected ising universal values a scaling analysis is performed on different types of numerical finite size data obtained by means of the transfer matrix method the results support ising universality a procedure based on conformal invariance reproduces the known ising temperature and magnetic exponents within 10 6 furthermore we estimate the critical density of the hard square model as rho c 0 367 743 000 5

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

equilibrium crystal shape of hard squares with diagonal attractions the author exactly calculates the anisotropic interfacial tension of a square lattice gas model with nearest neighbour exclusion and next nearest neighbour attractions this is achieved by a method which introduces the shift operator into the standard transfer matrix argument from the calculated anisotropic interfacial tension the equilibrium crystal shape ecs is derived by the use of the wulff construction the ecs is a closed curve in the x y plane represented as cosh lambda x y kbt a3cosh lambda x y kbt a4 2 0 with a scale factor lambda and constants a3 a4 he argues that this shape is a universal one which appears as the ecss of a wide class of models