Search results for "Ising Model"
showing 10 items of 241 documents
Absence of hyperscaling violations for phase transitions with positive specific heat exponent
1994
Finite size scaling theory and hyperscaling are analyzed in the ensemble limit which differs from the finite size scaling limit. Different scaling limits are discussed. Hyperscaling relations are related to the identification of thermodynamics as the infinite volume limit of statistical mechanics. This identification combined with finite ensemble scaling leads to the conclusion that hyperscaling relations cannot be violated for phase transitions with strictly positive specific heat exponent. The ensemble limit allows to derive analytical expressions for the universal part of the finite size scaling functions at the critical point. The analytical expressions are given in terms of generalH-fu…
Finite-size scaling approach for critical wetting: rationalization in terms of a bulk transition with an order parameter exponent equal to zero.
2012
Clarification of critical wetting with short-range forces by simulations has been hampered by the lack of accurate methods to locate where the transition occurs. We solve this problem by developing an anisotropic finite-size scaling approach and show that then the wetting transition is a ``bulk'' critical phenomenon with order parameter exponent equal to zero. For the Ising model in two dimensions, known exact results are straightforwardly reproduced. In three dimensions, it is shown that previous estimates for the location of the transition need revision, but the conclusions about a slow crossover away from mean-field behavior remain unaltered.
Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model.
2003
The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulations. Results for fixed boundary conditions are reported here, and compared with known results for periodic boundary conditions. Clear numerical evidence for ‘‘fat’’ stretched exponential tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature. Our work suggests that the true order-parameter distribution at the critical temperature must be considered to be unknown at present.
Models for highway traffic and their connections to thermodynamics
2007
Models for highway traffic are studied by numerical simulations. Of special interest is the spontaneous formation of traffic jams. In a thermodynamic system the traffic jam would correspond to the dense phase (liquid) and the free flowing traffic would correspond to the gas phase. Both phases depending on the density of cars can be present at the same time. A model for a single lane circular road has been studied. The model is called the optimal velocity model (OVM) and was developed by Bando, Sugiyama, et al. We propose here a reformulation of the OVM into a description in terms of potential energy functions forming a kind of Hamiltonian for the system. This will however not be a globally …
Wetting in fluid systems. Wetting and capillary condensation of lattice gases in thin film geometry
1994
Monte Carlo studies of lattice gas models with attractive interactions between nearest neighbors on a simple cubic lattice are carried out for a L×L×D geometry with two hard walls of size L×L and periodic boundary conditions parallel to the wall. Two types of short-range forces at the walls are considered: (i) Both walls are of the same type and exert an attractive force of the same strength (in Ising model terminology, surface fields HD = H1 occur). (ii) The walls differ, one attracts and the other repels particles, again with the same strength (HD = −H1). In the first case, capillary condensation occurs at a chemical potential differing from its value for phase coexistence in the bulk, an…
Parallelization of the Wolff single-cluster algorithm.
2010
A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have reached the speedup about 1.79 times …
?Almost? mean-field ising model: An algebraic approach
1991
We study the thermodynamic limit of the algebraic dynamics for an "almost" mean-field Ising model, which is a slight generalization of the Ising model in the mean-field approximation. We prove that there exists a family of "relevant" states on which the algebraic dynamics αt can be defined. This αt defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states. © 1991 Plenum Publishing Corporation.
Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
2013
We consider the superstable cycles of the Q-state Potts (QSP) and the three-site interaction antiferromagnetic Ising (TSAI) models on recursive lattices. The rational mappings describing the models' statistical properties are obtained via the recurrence relation technique. We provide analytical solutions for the superstable cycles of the second order for both models. A particular attention is devoted to the period three window. Here we present an exact result for the third order superstable orbit for the QSP and a numerical solution for the TSAI model. Additionally, we point out a non-trivial connection between bifurcations and superstability: in some regions of parameters a superstable cyc…
A universal tensor network algorithm for any infinite lattice
2018
We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which codifies the details of tensor networks on any graphs in any dimension $d$, we are able to produce a code that can be essentially launched to simulate any lattice. We further introduce an optimized algorithm to compute simple tensor updates as well as expectation values and correlators with a mean-field-like effective environments. Though not being variational, this strategy allows to cope with PEPS of very large bond dimension (e.g., $D=100$), and produces re…
Formation of Ordered Structures in Quenching Experiments: Scaling Theory and Simulations
1987
In this note we want to address the particular problem of the formation of ordered structures resulting from “quenching experiments”. The generic experimental situation is depicted in Figure 1. Initially the system is in an unordered random state in the one-phase region. Then the temperature is lowered (for some systems like polymers the coexistence curve is inverted so that the temperature must be raised) until the system is in the two phase region. The system is now in a non-equilibrium situation and evolves toward equilibrium. It is during the evolution toward equilibrium that the system develops ordered structures /1,2/.