duality relations and equilibrium crystal shapes of potts models on triangular and honeycomb lattices abstract we consider the q state potts models on triangular and honeycomb lattices for each lattice it is shown that the anisotropic interfacial tension is related to the anisotropic correlation length on the dual lattice using the star triangle transformation we also find that the anisotropic correlation length on the triangular lattice is the same as that of the honeycomb lattice for q 4 at the first order transition point the anisotropic correlation length is exactly calculated at the first order transition point by a method which introduces auxiliary edges into the models from the calculated anisotropic correlation length the equilibrium droplet shape of one ordered phase embedded inside another is derived via the wulff construction the equilibrium shape is written as a simple algebraic curve which corresponds to the dispersion relation of bound states in the terminology of spin chains

on positive semidefinite modification schemes for incomplete cholesky factorization incomplete cholesky factorizations have long been important as preconditioners for use in solving large scale symmetric positive definite linear systems in this paper we focus on the relationship between two important positive semidefinite modification schemes that were introduced to avoid factorization breakdown namely the approach of jennings and malik and that of tismenetsky we present a novel view of the relationship between the two schemes and implement them in combination with a limited memory approach we explore their effectiveness using extensive numerical experiments involving a large set of test problems arising from a wide range of practical applications

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

the covariance matrix of the potts model a random cluster analysis we consider the covariance matrix g mm q2 of thed dimensionalq states potts model rewriting it in the random cluster representation of fortuin and kasteleyn in any of theq ordered phases we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances thereby attributing algebraic significance to these stochastic geometric quantities we also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers for dimensiond 2 we show that this correlation length and the correlation length of the two point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two for systems with first order transitions this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self dual point o for systems with second order transitions this relation implies the equality of the correlation length exponents from above and below threshold as well as an amplitude ratio of two in the course of proving the above results we establish several properties of independent interest including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions and left continuity of the two dimensional free boundary condition percolation probability at o we also introduce dlr equations for the random cluster model and use them to establish ergodicity of the free measure in order to prove these results we introduce a new class of events which we call decoupling events and two inequalities for these events the first is similar to the fkg inequality but holds for events which are neither increasing nor decreasing the second is similar to the van den berg kesten inequality in standard percolation both inequalities hold for an arbitrary fkg measure

transfer matrix inverison identities for exactly solvable lattice spin models a new functional equation satisfied by the commuting row to row transfer matrices is derived for the eight vertex model functional equations of the same form are satisfied by hard hexagons magnetic hard squares the self dual potts models the andrews baxter forrester models and others these new functional equations are called inversion identities because they generalize the inversion relation for local transfer matrices it is conjectured that all solvable models satisfying yang baxter equations possess such inversion identities and that in general these functional equations can be solved for the transfer matrix eigenvalues

exact results for the zeros of the partition function of the potts model on finite lattices the yang lee zeros of the q state potts model are investigated in one two and three dimensions analytical results derived from the transfer matrix for the one dimensional model reveal a systematic behavior of the locus of zeros as a function of q for 1 2 they lie outside the unit circle for finite temperature in the special case q 2 the zeros lie exactly on the unit circle as proved by lee and yang in two and three dimensions the zeros are calculated numerically and behave in the same way results are also presented for the critical line of the potts model in an external field as determined from the zeros of the partition function in the complex temperature plane

on the phase diagram of the discrete z6 spin models we point out some problems with the previously proposed phase diagram of the z6 spin models consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies these deficiencies with the aid of a new parametrization of the phase space we study the models numerically with results which support our conjectures

the bethe ansatz for the six vertex model with rotated boundary conditions a method is suggested for derivation of the bethe ansatz equations for the six vertex model on a square lattice rotated at an arbitrary angle with respect to the coordinate axes the method is based on the random walk representation for configurations of the model the equations for the ice model on the rotated lattice are derived and some numerical results are obtained

hard hexagon model calculation of anisotropic interfacial tension from asymptotic degeneracy of largest eigenvalues of row row transfer matrix to find the directional dependence of the interfacial tension of the hard hexagon model an inhomogeneous system is studied this system is defined on a square lattice with 1 v m columns so that the lhs of the m 1 th column is the hard hexagon model and the rhs of the m 1 th column works as the operator which shifts the particle configuration of a column downward a triplet of the largest eigenvalues of the row row transfer matrix are asymptotically degenerate asm under the conditions that 1 v m 0 mod 3 withv being fixed to be constant the interfacial tension of a tilted interface is calculated from the finite correction terms in this limit

conformal spectrum of the six vertex model by way of a generalization of analytical methods recently introduced the conformal spectrum of the six vertex model with twisted boundary conditions is analysed nonlinear integral equations are derived from which all scaling dimensions and the spins can be extracted analytically in terms of rogers dilogarithms the scaling dimensions of low lying excitations are given by the so called gaussian dimensions

symmetry representations in the rigged hilbert space formulation of quantum mechanics we discuss some basic properties of lie group representations in rigged hilbert spaces in particular we show that a differentiable representation in a rigged hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of hilbert spaces we also construct a couple of examples illustrative of the key features of group representations in rigged hilbert spaces finally we establish a simple criterion for the integrability of an operator lie algebra in a rigged hilbert space

partial order in the self dual ashkin teller model corner transfer matrices are used to calculate the order parameters of the self dual ashkin teller model on the square lattice in the non critical regime it is found that the model is partially ordered i e the magnetisations s1 and t1 vanish while the polarisation s1t1 is non zero the polarisation which is given simply in terms of elliptic functions exhibits an essential singularity at criticality

hard squares with diagonal attractions the authors complete the solution of the square lattice gas with nearest neighbour exclusion and attractive next nearest neighbour diagonal interactions on the special surface corresponding to regimes iii and iv of the generalised hard hexagon model the interfacial tension correlation length and sublattice density difference are calculated throughout these regimes by obtaining the eigenvalues of the row to row and corner transfer matrices the associated critical exponents are found to be mu v 5 4 beta 3 32 in regime iii and mu v 5 2 beta 1 4 in regime iv in particular their results confirm the recent proposal by huse that regime iii is the first order coexistence surface separating the disordered fluid phase from the square ordered solid phases and that the regime iii regime iv boundary is a line of tricritical points

short time dynamics of cluster growth in the potts model the two and three dimensional q state potts model is simulated by a cluster algorithm and the relaxation dynamics of average cluster size and the order parameter during initial thermalization are studied the dependence of these quantities on the lattice size and q in the early stages of monte carlo iterations reveals valuable information on the nature of the phase transition occurring in the system from the initial thermalization data of the 2d 7 state potts model surface tension is also calculated the value is in good agreement with the exact result

3d symmetry detection using the extended gaussian image symmetry detection is important in the area of computer vision a 3d symmetry detection algorithm is presented in this paper the symmetry detection problem is converted to the correlation of the gaussian image once the gaussian image of the object has been obtained the algorithm is independent of the input format the algorithm can handle different kinds of images or objects simulated and real images have been tested in a variety of formats and the results show that the symmetry can be determined using the gaussian image

anisotropic correlation length in the eight vertex model we investigate the directional dependence or anisotropy of the correlation length of the eight vertex model by a method which introduces the shift operator into the usual transfer matrix argument for a given x 0 x 1 there are two cases with respect to a parameter q in the case 0 q x3 the anisotropic correlation length acl is independent of q noting that the eight vertex model factors into two ising lattices in the q x4 limit we can directly relate the acl to that of the square lattice ising model when x3 q x2 the acl depends on q using an algebraic curve we show that the acl in this case is connected with that of the ising model on a 4 8 or union jack lattice we suggest that a wide class of models have essentially the same acl as the eight vertex model has

hard hexagon model anisotropy of correlation length and interfacial tension the directional dependence of the correlation length of the hard hexagon model is calculated by a new method which introduces the shift operator into the usual transfer matrix method this method is also applied to the calculation of the interfacial tension of the hard hexagon model which is anisotropic in addition the equilibrium droplet shape of one phase embedded inside another is obtained from the analysis of the interfacial tension by the use of wulff s construction

adaptive techniques for improving the performance of incomplete factorization preconditioning three techniques for improving the robustness and performance of incomplete factorization preconditioners for sparse systems with symmetric positive definite or mildly indefinite coefficient matrices are introduced the primary contribution is two new block algorithms for incomplete factorization that result in an improvement in the performance of both the preconditioner generation and the iterative solution phases one of the algorithms applies to matrices that have a natural block structure in their original form and the other applies to matrices without natural dense blocks additionally two relatively simple but highly effective heuristic strategies are introduced these include selecting the solver based on the definiteness properties of the preconditioner and automatic selection and tuning of incomplete factorization parameters all three techniques have adaptive components i e the preconditioner solver combination chooses parameters or algorithmic components based on the properties of the coefficient matrix and its incomplete factors two of the three techniques are applicable to incomplete lu factorization for unsymmetric systems as well

the inversion relation method for some two dimensional exactly solved models in lattice statistics the partition functions per site of several two dimensional models notably the eight vertex self dual potts and hard hexagon models can be easily obtained by using an inversion relation for local transfer matrices together with symmetry and analyticity properties this technique is discussed the analyticity properties compared and some equivalences and nonequivalences pointed out in particular the critical hard hexagon model is found to have the same as the self dualq state potts model withq 3 5 2 2 618 the temperley lieb equivalence between the potts and six vertex models is found to fail in certain nonphysical antiferromagnetic cases

enhancing performance and robustness of ilu preconditioners by blocking and selective transposition incomplete factorization is one of the most effective general purpose preconditioning methods for krylov subspace solvers for large sparse systems of linear equations two techniques for enhancing the robustness and performance of incomplete lu factorization for sparse unsymmetric systems are described a block incomplete factorization algorithm based on the crout variation of lu factorization is presented the algorithm is suitable for incorporating threshold based dropping as well as unrestricted partial pivoting and it overcomes several limitations of existing incomplete lu factorization algorithms with and without blocking it is shown that blocking has a three pronged impact it speeds up the computation of incomplete factors and the solution of the associated triangular systems it permits denser and more robust factors to be computed economically and it permits a trade off with the restart parameter of gmres to further improve the overall speed and robustness a highly effective heuristic for imp

solving hermitian positive definite systems using indefinite incomplete factorizations incomplete ldl factorizations sometimes produce an indefinite preconditioner even when the input matrix is hermitian positive definite the two most popular iterative solvers for symmetric systems cg and minres cannot use such preconditioners they require a positive definite preconditioner one approach that has been extensively studied to address this problem is to force positive definiteness by modifying the factorization process we explore a different approach use the incomplete factorization with a krylov method that can accept an indefinite preconditioner the conventional wisdom has been that long recurrence methods like gmres or alternatively non optimal short recurrence methods like symmetric qmr and bicgstab must be used if the preconditioner is indefinite we explore the performance of these methods when used with an incomplete factorization but also explore a less known krylov method called pcg odir that is both optimal and uses a short recurrence and can use an indefinite preconditioner furthermore we propose another optimal short recurrence method called ip minres that can use an indefinite preconditioner and a variant of pcg odir which we call ip cg that is more numerically stable and usually requires fewer iterations

panorama a 3d shape descriptor based on panoramic views for unsupervised 3d object retrieval we present a novel 3d shape descriptor that uses a set of panoramic views of a 3d object which describe the position and orientation of the object s surface in 3d space we obtain a panoramic view of a 3d object by projecting it to the lateral surface of a cylinder parallel to one of its three principal axes and centered at the centroid of the object the object is projected to three perpendicular cylinders each one aligned with one of its principal axes in order to capture the global shape of the object for each projection we compute the corresponding 2d discrete fourier transform as well as 2d discrete wavelet transform we further increase the retrieval performance by employing a local unsupervised relevance feedback technique that shifts the descriptor of an object closer to its cluster centroid in feature space the effectiveness of the proposed 3d object retrieval methodology is demonstrated via an extensive consistent evaluation in standard benchmarks that clearly shows better performance against state of the art 3d object retrieval methods

reply to comment on equilibrium crystal shape of the potts model at the first order transition point the eight vertex model is defined on the square lattice rotated through an arbitrary angle with respect to the coordinate axes we re examine the analysis of the anisotropic correlation length in a previous paper fujimoto m 1996 physica a 233 485 502 we point out that the asymptotic form of the correlation function is expressed by the use of differential forms on a riemann surface of genus 1 combined with the symmetry of the square lattice this fact explains that the anisotropic correlation length is represented in terms of simple algebraic curves the argument is applicable to a wide class of lattice models including unsolvable ones

anisotropic interfacial tension and the equilibrium crystal shape of kagome lattice eight vertex model we exactly calculate the anisotropic interfacial tension of the kagome lattice eight vertex model with the help of two types of square lattice models each square lattice model is inhomogeneous but still possesses a one parameter family of commuting transfer matrices from the anisotropic interfacial tension the equilibrium shape of an inclusion of one ordered phase in an environment of another is obtained by applying the wulff construction calculations are expressed by the use of differential forms on a riemann surface of genus 1 and the equilibrium shape is written as an elliptic curve we suggest the possibility of interpreting critical phenomena in terms of the moduli space of riemann surfaces of genus 1

the spectra of q state vertex models and related antiferromagnetic quantum spin chains some exactly solvable q state vertex models are investigated the author employs inversion relations to determine directly the spectra of the transfer matrices in the thermodynamic limit by avoiding the more cumbersome bethe ansatz the results are applied to related quantum spin chains of which two families are su q and so q invariant respectively various quantities are calculated e g energy momentum excitations and the correlation length for q 3 the su q invariant chain is the pure biquadratic spin 1 hamiltonian which turns out to be non critical the ground state energy the gap and the correlation length are given

equilibrium crystal shape of the potts model at the first order transition point we investigate the q state two dimensional potts model the anisotropic interfacial tension is related by duality to the anisotropic correlation length for q 4 we calculate exactly the anisotropic correlation length at the first order transition point from the calculated anisotropic correlation length the equilibrium crystal shape ecs is derived via the wulff construction the ecs is expressed by means of a simple algebraic curve regarding q as a temperature scale we show that the potts model has the same ecs as the eight vertex model we discuss a connection between the ecs and the q deformed pseudo euclidian algebra

inversion identities for the self dual potts and ashkin teller models the commuting diagonal to diagonal transfer matrices of the self dual potts and ashkin teller models on the square lattice are shown to satisfy special functional equations called inversion identities these identities generalise the known local inversion or unitarity relations for interaction round a face or irf models satisfying yang baxter or star triangle equations

fast flat histogram method for generalized spin models we present a monte carlo method that efficiently computes the density of states for spin models having any number of interaction per spin by combining a random walk in the energy space with collective updates controlled by the microcanonical temperature our method yields dynamic exponents close to their ideal random walk values reduced equilibrium times and very low statistical error in the density of states the method can host any density of states estimation scheme including the wang landau algorithm and the transition matrix method our approach proves remarkably powerful in the numerical study of models governed by long range interactions where it is shown to reduce the algorithm complexity to that of a short range model with the same number of spins we apply the method to the q state potts chains 3 ensuremath leqslant q ensuremath leqslant 12 with power law decaying interactions in their first order regime we find that conventional local update algorithms are outperformed already for sizes above a few hundred spins by considering chains containing up to 2 16 spins which we simulated in fairly reasonable time we obtain estimates of transition temperatures correct to five figure accuracy finally we propose several efficient schemes aimed at estimating the microcanonical temperature

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

boundary conditions and inversion indentities for solvable lattice models with a sublattice symmetry the transfer matrices of solvable lattice spin models are considered under general boundary conditions associated with the symmetry of the models it is shown how the full symmetry can be exploited for systems having a sublattice symmetry by considering an extended model where the states distinguish the sublattices in this extended scheme the parity of the number of sites is tied to the boundary conditions the inversion identities can be extended and be used to obtain the full operator content of the critical models as an application the complete spectra of the transfer matrices for the eight vertex model at the decoupling point are calculated

comment on equilibrium crystal shape of the potts model at the first order transition point we comment on the paper by fujimoto 1997 j phys a math gen 30 3779 where the exact equilibrium crystal shape ecs in the critical q state potts model on the square lattice was calculated and its equivalence with ecs in the ising model was established we confirm these results giving their alternative derivation applying the transformation properties of the one particle dispersion relation in the six vertex model it is shown that this dispersion relation is identical to that in the ising model on the square lattice

the effects of the distribution of bimodal bonds on phase transition in 2d potts model abstract we have studied the q 8 state potts model in two dimension to determine the effects of the distribution of bimodal bonds on the phase transition we have shown that by monitoring the energy histograms and autocorrelation times there exist a finite size dependent threshold value of the introduced quenched bond randomness for rounding the first order phase transition and this threshold value becomes smaller as the system size increased

scaling dimensions and conformal anomaly in anisotropic lattice spin models the effect of anisotropic interactions on the eigenvalue spectrum of the row to row transfer matrix of critical lattice spin models is investigated it is verified that the predictions of conformal theory apply to anisotropic systems if one allows for spatial rescaling by incorporating an anisotropy factor zeta ay ax sin theta where ay and ax are lattice spacings and theta is an angle describing the anisotropy for exactly solvable models these anisotropy angles can be calculated analytically using corner transfer matrices this is done for the eight vertex model hard hexagons and interacting hard squares and it is found that theta pi u lambda 10u 3 and 5u respectively where u is the spectral parameter and lambda is the crossing parameter for each of these models the amplitude of the finite size corrections to the free energy at criticality is found to be of the form pi zeta c 6n2 where zeta is the anisotropy factor and the central charge or conformal anomaly is given by c 1 4 5 and 7 10 respectively this is an analytic result for the eight vertex model for the hard hexagon and square models the largest eigenvalues are found accurately by numerically solving their inversion identities for various anisotropies and strip widths up to n 48 finally the authors argue that the anisotropy angle for magnetic hard squares and the q state potts models is also given by theta pi u lambda so this result is quite general

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

vbarms a variable block algebraic recursive multilevel solver for sparse linear systems sparse matrices arising from the solution of systems of partial differential equations often exhibit a perfect block structure meaning that the nonzero blocks in the sparsity pattern are fully dense and typically small e g when several unknown quantities are associated with the same grid point similar block orderings can be sometimes unravelled also on general unstructured matrices by ordering consecutively rows and columns with a similar sparsity pattern and treating some zero entries of the reordered matrix as nonzero elements with a little sacrifice of memory we show how we can take advantage of these frequently occurring structures in the design of the multilevel incomplete lu factorization preconditioner arms saad and suchomel 2002 14 and maximize computational efficiency

evidences of the instability fixed points of first order phase transitions we study the dynamics of the first order phase transitions in the two dimensional potts model driven by a linearly varying temperature using a finite time scaling with extended dynamic monte carlo renormalization group method it is found that for sufficiently large lattice sizes the flows of apparent exponents of different temperature sweep rates upon renormalization show characteristics that are markedly distinct from those of continuous transitions and are argued to result from the instability fixed points involved and provide a method for estimating the associated instability exponents

efficient 3d shape matching and retrieval using a concrete radialized spherical projection representation we present a 3d shape retrieval methodology based on the theory of spherical harmonics using properties of spherical harmonics scaling and axial flipping invariance is achieved rotation normalization is performed by employing the continuous principal component analysis along with a novel approach which applies pca on the face normals of the model the 3d model is decomposed into a set of spherical functions which represents not only the intersections of the corresponding surface with rays emanating from the origin but also points in the direction of each ray which are closer to the origin than the furthest intersection point the superior performance of the proposed methodology is demonstrated through a comparison against state of the art approaches on standard databases

surface free energy of the critical six vertex model with free boundaries the bethe ansatz equations are derived for the six vertex model with general boundary weights on a lattice in a diagonal orientation these are solved in the thermodynamic limit finite size corrections to the free energy for a restricted class of boundary weights including those corresponding to a potts model with free boundaries are calculated in the critical region the first order term gives the surface free energy of the model the second order term is found to be pi okt tan pi nu 2 mu c 48n 2 where c 1 6 mu 2 pi 2 pi mu is the conformal anomaly this can be compared to pi kt sin pi nu mu c 6n 2 for a calculation on the lattice in the standard orientation and with periodic boundary conditions this difference can be explained geometrically using conformal invariance

an approximate and efficient method for optimal rotation alignment of 3d models in many shape analysis applications the ability to find the best rotation that aligns two models is an essential first step in the analysis process in the past methods for model alignment have either used normalization techniques such as pca alignment or have performed an exhaustive search over the space of rotation to find the best optimal alignment while normalization techniques have the advantage of efficiency providing a quick method for registering two shapes they are often imprecise and can give rise to poor alignments conversely exhaustive search is guaranteed to provide the correct answer but even using efficient signal processing techniques this type of approach can be prohibitively slow in this paper we present a new method for aligning two 3d shapes we show that the method is markedly faster than existing approaches based on efficient signal processing and we provide registration results demonstrating that the alignments obtained using our method have a high degree of precision and are markedly better than those obtained using normalization

rosy 3d object pose normalization based on pca and reflective object symmetry with application in 3d object retrieval a novel pose normalization method based on 3d object reflective symmetry is presented it is a general purpose global pose normalization method in this paper it is used to enhance the performance of a 3d object retrieval pipeline initially the axis aligned minimum bounding box of a rigid 3d object is modified by requiring that the 3d object is also in minimum angular difference with respect to the normals to the faces of its bounding box to estimate the modified axis aligned bounding box a set of predefined planes of symmetry are used and a combined spatial and angular distance between the 3d object and its symmetric object is calculated by minimizing the combined distance the 3d object fits inside its modified axis aligned bounding box and alignment with the coordinate system is achieved the proposed method is incorporated in a hybrid scheme that serves as the alignment method in a 3d object retrieval system the effectiveness of the 3d object retrieval system using the hybrid pose normalization scheme is evaluated in terms of retrieval accuracy and demonstrated using both quantitative and qualitative measures via an extensive consistent evaluation on standard benchmarks the results clearly show performance boost against current approaches

continuously varying exponents in magnetic hard squares the commuting row to row transfer matrices of magnetic hard squares on the multicritical t manifold are shown to satisfy a special functional equation called an inversion identity for strip widths up to n 32 these equations are solved numerically for the transfer matrix eigenvalues the central charge or conformal anomaly c 1 is obtained from 1 n2 corrections to the exact bulk free energy and scaling dimensions are obtained from the eigenvalue gaps the magnetic scaling dimension is xm 1 8 and the sublattice density difference scaling dimension is xe 1 9 2 y where y 2 lambda pi and the interaction dependent crossing parameter lambda varies between 0 and 2 pi 3 scaling dimensions for further operators fall in the sequence xn n2xe where n 1 2 3 4 the critical exponents also vary continuously along the multicritical line and are given by alpha 14 9y 16 9y beta m 9 2 y 16 16 9y beta e 1 2 16 9y nu 9 2 y 2 16 9y and delta 15 these exponents are simply related to the exponents of the critical eight vertex and ashkin teller models which also exhibit z2 z2 symmetry and the authors argue that these models lie in the same universality class

the correlation length of the potts model at the first order transition point the authors consider the q state two dimensional potts model for q g i e in the first order phase transition regime following a scheme given by p martin 1991 the authors prove an identity between the spectra of the transfer matrices of the potts model and the transfer matrices connecting the diagonals of a 6 vertex model by using a bethe ansatz for the latter they obtain an exact expression for the correlation length of the potts model at the transition point

an analytic treatment of finite size corrections in the spin 1 antiferromagnetic xxz chain it is known that the standard method for calculating finite size corrections in bethe ansatz solvable systems is not applicable to the takhtajan babujian model and its anisotropic xxz generalisation the authors develop a new analytic method explicitly avoiding root densities and associated problems nonlinear integral equations are derived whose solutions yield the correct central charges c 1 and c 3 2 for the spin 1 2 and spin 1 xxz chains respectively in the spin 1 case the authors obtain as a by product the finite size deviation of the bethe ansatz roots from the 2 string formation

the use of supernodes in factored sparse approximate inverse preconditioning in recent years the growing popularity of supercomputers has fostered the development of algorithms able to take advantage of the massive parallelism offered by multiple processors direct methods though robust and computationally efficient hardly exploit high degrees of parallelism by contrast krylov methods preconditioned by factored sparse approximate inverses fsai provide at least in principle a perfectly parallel approach but are often thwarted by an excessive set up cost in this paper we extend the concept of supernode from sparse lu factorizations to approximate inverses and use it to accelerate the computation of an fsai type preconditioner the numerical experiments on real world problems show that the overall fsai efficiency can be significantly increased while preserving its intrinsic parallelism

rectilinearity of 3d meshes in this paper we propose and evaluate a novel shape measure describing the extent to which a 3d polygon mesh is rectilinear the rectilinearity measure is based on the maximum ratio of the surface area to the sum of three orthogonal projected areas of the mesh it has the following desirable properties 1 the estimated rectilinearity is always a number from 0 1 2 the measure is invariant under scale rotation and translation 3 the 3d objects can be either open or closed meshes and we can also deal with degenerate meshes 4 the measure is insensitive to noise stable under small topology errors and robust against face deletion and mesh simplification moreover a genetic algorithm ga can be applied to compute the approximate rectilinearity efficiently we find that the calculation of rectilinearity can be used to normalize the pose of 3d meshes and in many cases it performs better than the principal component analysis pca based method by applying a simple selection criterion the combination of these two methods results in a new pose normalization algorithm which not only provides a higher successful alignment rate but also corresponds better with intuition finally we carry out several experiments showing that both the rectilinearity based pose normalization preprocessing and the combined signatures which consist of the rectilinearity measure and other shape descriptors can significantly improve the performance of 3d shape retrieval

row transfer matrix spectra of cyclic solid on solid lattice models the eigenvalue spectra of cyclic solid on solid csos row transfer matrices are studied an equivalence is established between the inversion identity and the bethe ansatz functional equations and these equations are solved in the thermodynamic limit by a wiener hopf perturbation technique for the bands of leading excitations thel state csos model with crossing parameter s l possesses a 2 l s fold degenerate largest eigenvalue corresponding to the 2 l s coexisting phases the expressions for the largest eigenvalue and free energy coincide with those of the eight vertex model the string excitations for 2s l admit different classifications and are treated separately the correlation length is calculated in both regimes yielding the critical exponentv l 2s in agreement with the scaling relations

auxiliary vertices method for kagome lattice eight vertex model we investigate a class of eight vertex models on a kagome lattice with the help of auxiliary vertices the kagome lattice eight vertex model kevm is related to an inhomogeneous system which leads to a one parameter family of commuting transfer matrices using an equation for commuting transfer matrices we determine their eigenvalues from calculated eigenvalues the correlation length of the kevm is derived with its full anisotropy there are two cases in the first case the anisotropic correlation length acl is the same as that of the triangular honeycomb lattice ising model by the use of an algebraic curve it is shown that the kagome lattice ising model the diced lattice ising model and the hard hexagon model also have essentially the same acl as the kevm in the second case we find that the acl displays 12fold rotational symmetry

eight vertex model anisotropic interfacial tension and equilibrium crystal shape the anisotropic interfacial tension of the eight vertex model is found by a new method which introduces two inhomogeneous systems as the width of the system becomes large a doublet of the largest eigenvalues of the row row transfer matrix is asymptotically degenerate the anisotropic interfacial tension is calculated from their finite size correction terms in this limit by the use of the anisotropic interfacial tension the equilibrium crystal shape of the eight vertex model is derived via wulff s construction the equilibrium crystal shape is represented as a simple algebraic curve we discuss the close relation between the algebraic curve and the form of an elliptic function appearing in the expression of the interfacial tension

symmetry identification of a 3 d object represented by octree an algorithm for identifying symmetry of a 3 d object given by its octree is presented and the symmetry degree a measure of object symmetry is proposed the algorithm is based on traversals of the octree obtained by the principal axis transform of an input octree an object can be in an arbitrary position and with arbitrary orientation within the octree space and a wide range of symmetries represented by groups of proper and improper rotations can be identified it is shown that the octree data structure supports these operations well especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry the operation of the algorithm is illustrated using some synthetic test objects the results which are composed of identified symmetry types and the corresponding symmetry degrees were satisfactory

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

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