Related papers: Generalized cluster algorithms for Potts lattice g…
We review the background of the cluster algorithms in Monte Carlo simulation of statistical physics problems. One of the first such successful algorithm was developed by Swendsen and Wang eight years ago. In contrast to the local…
In 1983, Aizenman, Chayes, Chayes, Fr\"ohlich, and Russo proved that $2$-dimensional Bernoulli plaquette percolation in $\mathbb{Z}^3$ exhibits a sharp phase transition for the event that a large rectangular loop is "bounded by a surface of…
We study the $q$-state ferromagnetic Potts model on the $n$-vertex complete graph known as the mean-field (Curie-Weiss) model. We analyze the Swendsen-Wang algorithm which is a Markov chain that utilizes the random cluster representation…
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of…
We demonstrate that the invaded cluster algorithm, recently introduced by Machta et al, is a fast and reliable tool for determining the critical temperature and the magnetic critical exponent of periodic and aperiodic ferromagnetic Ising…
Local constraint is closely related to the gauge field, so constrained models are usually effective low energy descriptions and important in condensed matter physics. On the other hand, local restriction hinders the application of numerical…
We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the $q$-state Potts model, and the classical XY model. As for the…
A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape…
We present cluster Monte Carlo algorithms for the $XYZ$ quantum spin models. In the special case of $S=1/2$, the new algorithm can be viewed as a cluster algorithm for the 8-vertex model. As an example, we study the $S=1/2$ $XY$ model in…
We study the performance of Monte Carlo simulations that sample a broad histogram in energy by determining the mean first-passage time to span the entire energy space of d-dimensional ferromagnetic Ising/Potts models. We first show that…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates…
Potts spin systems play a fundamental role in statistical mechanics and quantum field theory, and can be studied within the spin, the Fortuin-Kasteleyn (FK) bond or the $q$-flow (loop) representation. We introduce a Loop-Cluster (LC) joint…
A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional +/-J…
We introduce a parallel Wang-Landau method based on the replica-exchange framework for Monte Carlo simulations. To demonstrate its advantages and general applicability for simulations of complex systems, we apply it to different spin models…
Coupled cluster theory is a vital cornerstone of electronic structure theory and is being applied to ever-larger systems. Stochastic approaches to quantum chemistry have grown in importance and offer compelling advantages over traditional…
The self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of devised simulation method is the artificial dynamics consisting of the single-spin-flip algorithm of Metropolis…
We apply extensive Monte Carlo simulations to study the probability distribution $P(m)$ of the order parameter $m$ for the simple cubic Ising model with periodic boundary condition at the transition point. Sampling is performed with the…
We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We…
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-replica cluster method and is much more efficient than the…
The cluster algorithm in the fully frustrated Ising model on the square lattice is essentially different from the ones used in other systems. Thus its better understanding is particularly important for finding new lines of development.…