Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Fixed-cluster acceleration algorithm for spin systems

Tanniemola B. Liverpool, Sharon C. Glotzer

Published May 1, 1996• 15 citations
Publisher

Abstract

A recently introduced cluster acceleration algorithm for spin models [J. Machta et al., Phys. Rev. Lett. 75, 2792 (1995)] based on invasion percolation is generalized to temperatures away from the critical point using concepts of random bond percolation. The generalized algorithm is equivalent to an "optimized" version of the Swendsen-Wang cluster algorithm [R. H. Swendsen and J. S. Wang, Phys. Rev. Lett. 58, 86 (1987)], and we demonstrate its success and speed at all temperatures for the $d=2$ Ising model. We argue that the previously discussed connection to self-organized criticality may be viewed as one limit of the fixed-cluster algorithm.

DOI
10.1103/physreve.53.r4255

Related papers

Invaded Cluster Algorithm for Equilibrium Critical Points

Jonathan L. Machta, Y. S. Choi, A. Lücke +2 more

A new cluster algorithm based on invasion percolation is described. The algorithm samples the critical point of a spin system without a priori knowledge of the critical temperature and provides an efficient way to determine the critical temperature and other observables in the critical region. The method is illustrated for the two- and three-dimensional Ising models. The algorithm equilibrates spin configurations much faster than the closely related Swendsen-Wang algorithm.

arXiv:cond-mat/9507094•Physical Review Letters•Oct 9, 1995•77 citations

ScalingAnsatzfor Swendsen-Wang Dynamics

W. Klein, Tane S. Ray, Pablo Tamayo

Using cluster and percolation concepts, we obtain a relation between relaxation times at critical points obtained from a new dynamical model introduced by Swendsen and Wang and those obtained from Glauber dynamics. This relation, which involves only static critical exponents, provides new insight into the physics underlying cluster acceleration methods such as the one introduced by Swendsen and Wang.

Physical Review Letters•Jan 9, 1989•37 citations

Critical dynamics of cluster algorithms in the random-bond Ising model

Ulvi Kanbur, Zeynep Demir Vatansever

In the present work, we present an extensive Monte Carlo simulation study on the dynamical properties of the two-dimensional random-bond Ising model. The correlation time τ of the Swendsen-Wang and Wolff cluster algorithms is calculated at the critical point. The dynamic critical exponent z of both algorithms is also measured by using the numerical data for several lattice sizes up to L=512. It is found for both algorithms that the autocorrelation time decreases considerably and the critical slowing-down effect reduces upon the introduction of bond disorder. Additionally, simulations with the Metropolis algorithm are performed, and the critical slowing-down effect is observed to be more pronounced in the presence of disorder, confirming the previous findings in the literature. Moreover, the existence of the non-self-averaging property of the model is demonstrated by calculating the scaled form of the standard deviation of autocorrelation times. Finally, the critical exponent ratio of the magnetic susceptibility is estimated by using the average cluster size of the Wolff algorithm.

Physical review. E•Feb 28, 2024•2 citations

Virtual bond percolation for Ising cluster dynamics

Richard C. Brower, Pablo Tamayo

The Fortuin-Kasteleyn mapping between the Ising model and the site-bond correlated percolation model is shown to be only one of an infinite class of exact mappings. These new cluster representations are a result of "renormalized" percolation rules correlated to entire blocks of spins. For example these rules allow for percolation on "virtual" bonds between spins not present in the underlying Hamiltonian. As a consequence we can define new random cluster theories each with its own Monte Carlo cluster dynamics that exactly reproduce the Ising model. By tuning parameters on the critical percolation surface, it is demonstrated numerically that cluster algorithms can be formulated for the 2-d and 3-d Ising model that have smaller autocorrelations than the original Swendsen-Wang algorithm.

arXiv:hep-lat/9206007•Physica A Statistical Mechanics and its Applications•Apr 1, 1993•9 citations

Efficient simulation of the random-cluster model

Eren Metin Elçi, Martin Weigel

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 Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.

arXiv:1307.6647•Physical Review E•Sep 16, 2013•17 citations

Critical clusters and efficient dynamics for frustrated spin models

V. Cataudella, Giancarlo Franzese, Mario Nicodemi +2 more

A general method to find, in a systematic way, efficient Monte Carlo cluster dynamics among the vast class of dynamics introduced by Kandel et al. [Phys. Rev. Lett. 65, 941 (1990)] is proposed. The method is successfully applied to a class of frustrated two-dimensional Ising systems. In the case of the fully frustrated model, we also find the intriguing result that critical clusters consist of self-avoiding walk at the \ensuremath{\theta} point.

Physical Review Letters•Mar 7, 1994•45 citations
A recently introduced cluster acceleration algorithm for spin models [J. Machta et al., Phys. Rev. Lett. 75, 2792 (1995)] based on invasion percolation is generalized to temperatures away from the critical point using concepts of random bond percolation. The generalized algorithm is equivalent to an "optimized" version of the Swendsen-Wang cluster algorithm [R. H. Swendsen and J. S. Wang, Phys. Rev. Lett. 58, 86 (1987)], and we demonstrate its success and speed at all temperatures for the d=2d=2d=2 Ising model. We argue that the previously discussed connection to self-organized criticality may be viewed as one limit of the fixed-cluster algorithm.
In the present work, we present an extensive Monte Carlo simulation study on the dynamical properties of the two-dimensional random-bond Ising model. The correlation time τ of the Swendsen-Wang and Wolff cluster algorithms is calculated at the critical point. The dynamic critical exponent z of both algorithms is also measured by using the numerical data for several lattice sizes up to L=512. It is found for both algorithms that the autocorrelation time decreases considerably and the critical slowing-down effect reduces upon the introduction of bond disorder. Additionally, simulations with the Metropolis algorithm are performed, and the critical slowing-down effect is observed to be more pronounced in the presence of disorder, confirming the previous findings in the literature. Moreover, the existence of the non-self-averaging property of the model is demonstrated by calculating the scaled form of the standard deviation of autocorrelation times. Finally, the critical exponent ratio of the magnetic susceptibility is estimated by using the average cluster size of the Wolff algorithm.
The Fortuin-Kasteleyn mapping between the Ising model and the site-bond correlated percolation model is shown to be only one of an infinite class of exact mappings. These new cluster representations are a result of "renormalized" percolation rules correlated to entire blocks of spins. For example these rules allow for percolation on "virtual" bonds between spins not present in the underlying Hamiltonian. As a consequence we can define new random cluster theories each with its own Monte Carlo cluster dynamics that exactly reproduce the Ising model. By tuning parameters on the critical percolation surface, it is demonstrated numerically that cluster algorithms can be formulated for the 2-d and 3-d Ising model that have smaller autocorrelations than the original Swendsen-Wang algorithm.
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 Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.