Related papers: Probability-Changing Cluster Algorithm for Potts M…
We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the $q$-state Potts model to non-integer values $q>1$. Its results…
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…
The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the…
Herein, we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the…
We review the local Monte Carlo dynamics and Swendsen-Wang cluster algorithm. We introduce and analyze a new Monte Carlo dynamics known as transitional Monte Carlo. The transitional Monte Carlo algorithm samples energy probability…
The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface order parameters and susceptibilities and…
In this paper we lay special stress on analyzing the topological properties of the lattice systems and try to ovoid the conventional ways to calculate the critical points. Only those clusters with finite sizes can execute the self similar…
Many spin systems affected by critical slowing down can be efficiently simulated using cluster algorithms. Where such systems have long-range interactions, suitable formulations can additionally bring down the computational effort for each…
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…
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 propose an extension of the nonequilibrium invaded cluster (IC) algorithm, which reestablishes a correct scaling of fluctuations at criticality and also self-adjusts to the critical temperature. We show that by introducing a single…
I propose a numerical simulation algorithm for statistical systems which combines a microcanonical transfer of energy with global changes in clusters of spins. The advantages of the cluster approach near a critical point augment the speed…
In this article we create a new algorithm for the perfect simulation of the infinite Potts model at a sufficiently small or at a sufficiently high temperature, in particular under the transition phase temperature. We study the model for…
We consider the two dimensional $Q-$ random-cluster Potts model on the torus and at the critical point. We study the probability for two points to be connected by a cluster for general values of $Q\in [1,4]$. Using a Conformal Field Theory…
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…
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…
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…
We implement a cluster-update Monte Carlo algorithm to simulate magnetic dipoles of the XY-spin type confined in a two-dimensional plane. The long-range character and anisotropy in the dipole interaction are handled by using the…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…