相关论文: A Cluster Method for the Ashkin--Teller Model

We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This…

In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…

The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full…

The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the…

We simulate the kinetic Ashkin-Teller model with both ordered and disordered initial states, evolving in contact with a heat-bath at the critical temperature. The power law scaling behaviour for the magnetic order and electric order are…

A cluster algorithm is presented for the $Z_2$ Kalb-Ramond plaquette model in four dimensions which dramatically reduces critical slowing. The critical exponent $z$ is reduced from $ z>2$ (standard Metropolis algorithm) to $z= 0.32\pm0.06$.…

The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the…

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin--Teller model. We find that the Li--Sokal bound on the autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$) holds along the…

An algorithm for Monte Carlo simulations is proposed in which the parameter controlling the strength of the transition becomes a dynamical variable and in which efficient transitions are achieved by cluster steps. It allows to avoid the…

We consider two critical semi-infinite subsystems with different critical exponents and couple them through their surfaces. The critical behavior at the interface, influenced by the critical fluctuations of the two subsystems, can be quite…

The edge-cubic spin model on square lattice is studied via Monte Carlo simulation with cluster algorithm. By cooling the system, we found two successive symmetry breakings, i.e., the breakdown of $O_h$ into the group of $C_{3h}$ which then…

A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes…

An overview is given over the recently developed and now widely used Monte Carlo algorithms with reduced or eliminated critical slowing down. The basic techniques are overrelaxation, cluster algorithms and multigrid methods. With these…

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of…

We develop cluster algorithms for a broad class of loop models on two-dimensional lattices, including several standard O(n) loop models at n \ge 1. We show that our algorithm has little or no critical slowing-down when 1 \le n \le 2. We use…

We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an $XY$ model into the target model, and we study its mathematical properties for a variety of nonlinear $\sigma$-models. We then apply the method…

We present a self consistent method based on cluster algorithms and Renormalization Group on the lattice to study critical systems numerically. We illustrate it by means of the 2D Ising model. We compute the critical exponents $\nu$ and…

The Ashkin-Teller (AT) model is a generalization of Ising 2-d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via a four-spin interaction. It was conjectured…

We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three colour model, appears to have a dynamic exponent close to zero, making it…

We study a generalized clock model on the simple cubic lattice. The parameter of the model can be tuned such that the amplitude of the leading correction to scaling vanishes. In the main part of the study we simulate the model with $Z_8$…