Showing papers on "Potts model published in 1994"
TL;DR: The domain dynamics of a quenched system with many nonconserved order parameters was investigated by using the time-dependent Ginzburg-Landau kinetic equations and produced microstructures remarkably similar to experimental observations of normal grain growth.
Abstract: The domain dynamics of a quenched system with many nonconserved order parameters was investigated by using the time-dependent Ginzburg-Landau kinetic equations. Our computer simulation of a model two-dimensional system produced microstructures remarkably similar to experimental observations of normal grain growth. After a short transient, the average domain or grain radius was found to increase with time as ${\mathit{t}}^{1/2}$, in agreement with most of previous mean-field predictions and more recent Q-state Potts model Monte Carlo simulations.
380 citations
TL;DR: In this article, a functional integral representation of the ground states of quantum spin chains is presented with the help of functional integral analysis of the system's equilibrium states, including the possibility of dimerization, conditions for the existence of a spectral gap, and a dichotomy analogous to one found by Affleck and Lieb.
Abstract: A number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system's equilibrium states. Methods of general applicability are introduced in the context of the SU(2S+1)-invariant quantum spin-S chains with the interaction −P(o), whereP(o) is the projection onto the singlet state of a pair of nearest neighbor spins. The phenomena discussed here include: the absence of Neel order, the possibility of dimerization, conditions for the existence of a spectral gap, and a dichotomy analogous to one found by Affleck and Lieb, stating that the systems exhibit either slow decay of correlations or translation symmetry breaking. Our representation elucidates the relation, evidence for which was found earlier, of the −P(o) spin-S systems with the Potts and the Fortuin-Kasteleyn random-cluster models in one more dimension. The method reveals the geometric aspects of the listed phenomena, and gives a precise sense to a picture of the ground state in which the spins are grouped into random clusters of zero total spin. E.g., within such structure the dichotomy is implied by a topological argument, and the alternatives correspond to whether, or not, the clusters are of finite mean length.
182 citations
TL;DR: In this paper, the boundary height distributions of the two-dimensional Abelian sandpile model are studied in the self-organized critical state and the leading asymptotic term of the corresponding correlation functions is observed to behave as r-4 when r to infinity.
Abstract: Boundary height distributions of the two-dimensional Abelian sandpile model are studied in the self-organized critical state. All height probabilities are calculated explicitly both at open and closed boundaries. The leading asymptotic term of the corresponding correlation functions is observed to behave as r-4 when r to infinity . On the basis of conformal field theory predictions the bulk height correlators are shown to have the same critical exponents as boundary ones. All heights seem to be identified with appropriate counterparts of the local energy operator in the zero-component Potts model.
46 citations
TL;DR: The dilute A3 model is a solvable lattice model with a critical point in the Ising universality class as mentioned in this paper, where the parameter by which the model can be taken away from the critical point acts like a magnetic field by breaking the Z2 symmetry between the states.
43 citations
TL;DR: In this article, the Fortuin-Kasteleyn representation of Potts models with many-body interactions was used to obtain necessary and sufficient conditions on the set of interactions of such a Potts model in order that its critical point be a monotonic function of the strengths of interactions.
Abstract: Known differential inequalities for certain ferromagnetic Potts models with pair interactions may be extended to Potts models with many-body interactions. As a major application of such differential inequalities, we obtain necessary and sufficient conditions on the set of interactions of such a Potts model in order that its critical point be astrictly monotonic function of the strengths of interactions. The method yields some ancillary information concerning the equality of certain critical exponents for Potts models; this amounts to a small amount of rigorous universality. These results are achieved in the context of a “Fortuin-Kasteleyn representation” of Potts models with many-body interactions. For such a Potts model, the corresponding random-cluster process is a (random) hypergraph.
42 citations
TL;DR: The cluster-variation method implies the existence of three phase transitions in the antiferromagnetic Potts model on the simple-cubic lattice.
Abstract: Using the cluster-variation method we study the phase diagram of the Blume-Emergy-Griffiths (BEG) model on simple cubic and face-centered cubic lattices. For the simple cubic lattice the main attention is paid to reentrant phenomena and ferrimagnetic phases occurring in a certain range of coupling constants. The results are in close agreement with Monte-Carlo data, available for parts of the phase diagram. Several ferrimagnetic phases are obtained in the vicinity of the line in parameter space, at which the model reduces to the antiferromagnetic three-state Potts model. Our results imply the existence of three phase transitions in the antiferromagnetic Potts model on the simple-cubic lattice. The phase diagrams for the BEG model on the face-centered cubic lattice are obtained in the region of antiquadrupolar ordering. Also the several ordered phases of the antiferromagnetic Potts model on this lattice are discussed.
41 citations
TL;DR: In this article, the authors determined the interface free energy Fo.d. between disordered and ordered phases in the q = 10 and q = 20 2d Potts models using the results of multicanonical Monte Carlo simulations on L2 lattices, and suitable finite-volume estimators.
37 citations
TL;DR: In this article, the authors obtained new fermionic sum representations for the Virasoro characters of the conformal field theory describing the ferromagnetic three-state Potts spin chain.
Abstract: We obtain new fermionic sum representations for the Virasoro characters of the conformal field theory describing the ferromagnetic three-state Potts spin chain. These arise from the fermionic quasiparticle excitations derived from the Bethe equations for the eigenvalues of the Hamiltonian. In the conformal scaling limit, the Bethe equations provide a description of the spectrum in terms of one genuine quasiparticle and two “ghost” excitations with a limited microscopic momentum range. This description is reflected in the structure of the character formulas, and suggests a connection with the integrable perturbation of dimensions (2/3, 2/3)+ which breaks theS3 symmetry of the conformal field theory down toZ2.
37 citations
TL;DR: The zeros of the partition function in the one-dimensional q-state Potts model with arbitrary and continuous q>or=0 have been studied using a transfer matrix in this paper.
Abstract: The zeros of the partition function in the one-dimensional q-state Potts model with arbitrary and continuous q>or=0 have been studied using a transfer matrix. The location of zeros and the Yang-Lee edge singularity have been analysed, and two different regimes, corresponding to q>1 and q>1, have been observed. A duality relation has also been derived, which relates the zeros in the complex field plane to those in the complex temperature plane.
36 citations
TL;DR: In this article, the interfadal tension of the general solvable N-state chiral Potts model was obtained, and it was shown that it has exponent (N + 2)/(2N) in the horizontal and vertical directions, in agreement with the scaling relation 2p = 2 -U.
Abstract: We obtain the interfadal tension of the general solvable N-state chiral Potts model. It has exponent @ = (N + 2)/(2N) in bath the horizontal and vertical directions, in agreement with the scaling relation 2p = 2 -U. 1. Jlltr~uctiou
33 citations
TL;DR: In this paper, the authors used the numerical data to show that the transition is first-order, and estimate the latent heat, the discontinuity in the magnetization, and a number of other critical parameters.
Abstract: For paper II, see ibid, vol. 27, p.1503 (1994). The finite-lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the 3-state Potts model on the simple cubic lattice to order z43 and the high-temperature expansion of the partition function to order v21. We use the numerical data to show that the transition is first-order, and estimate the latent heat, the discontinuity in the magnetization, and a number of other critical parameters.
TL;DR: In this paper, the q-state Potts model was used to extend low-temperature series for the partition function, order parameter and susceptibility of the Q-State Potts Model to order z56 (i.e., u28), z47, z43, z39, Z39, z 39, z35, z31 and z31 for q = 2, 3, 4, 4 and 9 respectively.
Abstract: The finite-lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the q-state Potts model to order z56 (i.e. u28), z47, z43, z39, z39, z39, z35, z31 and z31 for q=2, 3, 4, ..., 9 and 10 respectively. These series are used to test techniques designed to distinguish first-order transitions from continuous transitions. New numerical values are also obtained for the q-state Potts model with q>4.
CERN1
TL;DR: In this article, the authors presented the results of a Monte Carlo study of the three-dimensional antiferromagnetic three-state Potts model with periodic and anti-periodic boundary conditions in a neighborhood of the critical coupling.
Abstract: We present the results of a Monte Carlo study of the three-dimensionalXY model and the three-dimensional antiferromagnetic three-state Potts model. In both cases we compute the difference of the free energies of a system with periodic and a system with antiperiodic boundary conditions in a neighborhood of the critical coupling. From the finite-size scaling behaviour of this quantity we extract values for the critical temperature and the critical exponentv that are compatible with recent high-statistics Monte Carlo studies of the models. The results for the free energy difference at the critical temperature and for the exponentv confirm that both models belong to the same universality class.
TL;DR: In this article, both the ferromagnetic and antiferromagnetic models were investigated with the aid of simulations. But the results for thin graphs were not compared with those for higher-state Potts models and Ising models on fat graphs.
TL;DR: In this paper, the antiferromagnetic Potts model in the magnetic field is rigorously considered on the Bethe lattice by means of a recursion relation, which allows one to study the critical properties of the model as the properties of an iteration sequence { x n } in the limit n → ∞.
TL;DR: In this paper, the authors compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-state Potts model with random bonds at the critical point.
Abstract: We compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach for the perturbation series around the conformal field theories representing the pure models. We obtain corrections for the correlations functions which produce crossover in the amplitude but don't change the critical exponent in the case of the Ising model and which produce a shift in the critical exponent, due to randomness, in the case of the Potts model. Comparison with numerical data is discussed briefly.
CERN1
TL;DR: In this paper, the authors present the results of a Monte Carlo study of the 3D anti-ferromagnetic 3-state Potts model and compare the results with a recent high statistics study of 3D XY model strongly support the hypothesis that both models belong to the same universality class.
Abstract: We present the results of a Monte Carlo study of the three-dimensional anti-ferromagnetic 3-state Potts model. We compute various cumulants in the neighborhood of the critical coupling. The comparison of the results with a recent high statistics study of the 3D XY model strongly supports the hypothesis that both models belong to the same universality class. From our numerical data of the anti-ferromagnetic 3-state Potts model we obtain for the critical coupling K c = 0.81563(3), and for the static critical exponents γ / v = 1.973(9) and v = 0.664(4).
TL;DR: In this paper, the authors studied the phase diagram of an isotropic six-state chiral Potts model on a square lattice by means of both exact and numerical methods.
Abstract: We study the phase diagram of an isotropic six-state chiral Potts model on a square lattice by means of both exact and numerical methods. The phase diagram of this model presents many similarities with the phase diagrams of the Ashkin-Teller model or the models studied by Zamolodchikov and Monarstirskii. A remarkable line globally invariant under a transformation generalizing the Kramers-Wannier duality seems to correspond to a first order transition line up to a bifurcation point where this line splits into two second order lines. All the numerical calculations are compared with exact results which can be performed using a canonical elliptic parametrization of this model. The bifurcation point is found to correspond to the intersection of a generalized self-dual line with an algebraic curve. This curve corresponds to the set of points of the phase diagram for which a non-trivial infinite symmetry group of the model degenerates into a finite group of order six. The agreement between numerical and analytical results is very good.
TL;DR: In this paper, the authors comment on the diagonalization of the XXZ chain Hamiltonian using the abstract Temperley-Lieb algebra relations, following the paper by Dan Levy1 where the idea was first developed.
Abstract: The purpose of this note is to comment on the diagonalization of the XXZ chain Hamiltonian (and others such as the Potts model), using the abstract Temperley-Lieb algebra relations, following the paper by Dan Levy1 where the idea was first developed.
TL;DR: The variational problem for the Curie-Weiss-Potts model is solved completely in this article, and all the solutions of the variational problems are non-degenerate points, so all the results in Ellis and Wang (1990, 1992) can be easily extended to the case considered here.
TL;DR: In this paper, the authors constructed fused critical D, E and elliptic D models with bond variables on the edges of faces in addition to the spin variables on corners and showed that the row transfer matrices of the fused models satisfy special functional equations.
Abstract: Fusion hierarchies of A-D-E face models are constructed. The fused critical D, E and elliptic D models yield new solutions of the Yang-Baxter equations with bond variables on the edges of faces in addition to the spin variables on the corners. It is shown directly that the row transfer matrices of the fused models satisfy special functional equations. Intertwiners between the fused A-D-E models are constructed by fusing the cells that intertwine the elementary face weights. As an example, we calculate explicitly the fused 2×2 face weights of the 3-state Potts model associated with the D4 diagram as well as the fused intertwiner cells for the A5-D4 intertwiner. Remarkably, this 2×2 fusion yields the face weights of both the Ising model and 3-state CSOS models.
TL;DR: In this article, the two-point scalar operators (TPSO) are computed using U q [SU(2)] tensor calculus and their averages on the ground state give the two point correlation functions.
TL;DR: The invention is particularly characterized in that between the first suction cylinders and the delivery discs there are provided a second and third suction cylinder preceded by an adjustable stop abutment and a flap opener and associated with a folding pocket and a folding cylinder.
Abstract: It is shown that unless NP collapses to random polynomial time RP, there can be no fully polynomial randomised approximation scheme for the antiferromagnetic version of the Q-state Potts model.
TL;DR: In this paper, a new model of normal grain growth in two-dimensional systems is derived from considerations of Potts model simulations, based on Hillert's theory and combines the essential topological features of the grain boundary network with the action of capillarity.
Abstract: A new model of normal grain growth in two-dimensional systems is derived from considerations of Potts model simulations. This Randomly Connected Bubble model is based on Hillert's theory and combines the essential topological features of the grain boundary network with the action of capillarity. It succesfully predicts what the scaling state of the network should be and explains why the system evolves into this state. The implications for grain growth in real materials are also discussed.
TL;DR: The asymptote for Q' to infinity is found, and it is shown that for K=0 the information gain per coupling, Delta I=( alpha c In Q')/(Q'-1), converges slowly to 1/2 in this limit.
Abstract: By means of a general formulation for the optimal learning capacity of perceptrons with multi-state neurons and real-valued couplings with spherical constraints, which we derive by a cavity method, we calculate the optimal learning capacity alpha c(Q', K) :=pmax/(N(Q-1)) for perceptrons with a Q-resp. Q'-state Potts-model input resp. output neurons as a function of Q' and the stability parameter K. Among other results, the asymptote for Q' to infinity is found, and it is shown that for K=0 the information gain per coupling, Delta I=( alpha c In Q')/(Q'-1), converges slowly to 1/2 in this limit. Moreover, for Q' to infinity the same asymptotics also apply for the simple case of Hebbian learning.
TL;DR: The static and dynamic properties of the frustrated percolation model are investigated in this article, which contains frustration as an essential ingredient, exhibits two transitions: one at a temperature T p with critical exponents of the Potts model, and a second transition at a lower temperature T g in the same universality class of the Ising spin glass model.
Abstract: The static and dynamic properties of the frustrated percolation model are investigated. This model, which contains frustration as an essential ingredient, exhibits two transitions: a percolation transition at a temperatureT p with critical exponents of the ferromagnetic (s=1/2)-state Potts model, and a second transition at a lower temperatureT g in the same universality class of the Ising spin glass model. AboveT p the time-dependent autocorrelation function is characterized by a single exponential, while forT p>T>T g preliminary numerical results show a broad shoulder or plateau typical of a structural glass transition. BelowT g the system is in glassy state with an infinitely long relaxation time.
TL;DR: In this article, the spectrum and correlation functions of the general Zn-spin quantum chain were derived for the massive low-temperature phase of the Z3-chiral Potts quantum chain.
Abstract: Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z3-chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground-state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Zn-spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z3 model we are able to gain some insight into correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.
TL;DR: In this paper, the authors study the complete phase diagram of a model of interacting branched polymers and conjecture the existence of two different universality classes for the theta transitions (with thermal exponents, nu and phi, equal to ( 1/2, 2/3) and (8/15, 8/15) separated by a higher-order percolation point.
Abstract: In this paper we study the complete phase diagram of a model of interacting branched polymers. The model we consider is a lattice animal one, where the collapse transition can be driven both by a contact fugacity between two occupied nearest neighbours and by a fugacity related to each occupied edge. Using a Potts model formulation of the problem we conjecture the existence of two different universality classes for the theta transitions (with thermal exponents, nu and phi , equal to ( 1/2 , 2/3) and (8/15, 8/15) Separated by a higher-order percolation point. We also present convincing numerical evidence for these exponent values using a transfer-matrix approach. We discuss the possibility of a collapse-collapse transition and we predict the behaviour of our model when an adsorbing surface is included.
TL;DR: Inversion relations for the standard q-state triangular Potts model with two-and three-spin interactions were obtained in this paper, and it was shown that these inversion relations generate a group of symmetries of the model which is naturally represented in terms of birational transformations in a four dimensional parameter space.
Abstract: Inversion relations are obtained for the standard scalar q-state triangular Potts model with two- and three-spin interactions, generalizing previously known results for two-spin interaction models. It is shown that these inversion relations generate a group of symmetries of the model which is naturally represented in terms of birational transformations in a four dimensional parameter space. This group of birational transformations is generically a very large one, namely a hyperbolic Coxeter group. In this framework of very large groups of symmetries, a remarkable situation pops out: the one for which q corresponds to Tutte-Beraha numbers.
TL;DR: In this article, the q = 3 Potts model in three dimensions by Monte Carlo simulations is considered and the microcanonical density of states Ω is calculated as a function of the internal energy e of the system.
Abstract: We consider theq=3 Potts model in three dimensions by Monte Carlo simulations. The microcanonical density of states Ω is calculated as a function of the internal energy e of the system. We extrapolate the data for the simulated finite systems to the thermo-dynamic limit and find a discontinuous phase transition. This method is checked in the two-dimensional case, where exact results are known.