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

Critical relaxation in two-dimensional random-bond Potts models

S. Chen, David Paul Landau

Published Jan 1, 1997• 3 citations
Publisher

Abstract

We present an extensive Monte Carlo study of the critical relaxation for the two-dimensional square lattice random-bond Potts model using Swendsen-Wang cluster flipping. The integrated autocorrelation time \ensuremath{\tau} is calculated and the dynamic exponent z is estimated by analyzing the size dependence of \ensuremath{\tau}. We find that z\ensuremath{\approx}0 in agreement with estimates for the two-dimensional Ising model. We also present a study of the size dependence of the dynamic behavior of the pure eight-state Potts model which undergoes a first-order transition. The scaling is describable by the product of an exponential times a power law, a behavior which is quite different from that found in the random-bond case.

DOI
10.1103/physreve.55.40

Related papers

Dynamical critical properties of the random-bond three-state Potts model

Anonymous, Ulvi Kanbur, Mohammad Sadra Najafi +2 more

We study the dynamic critical behavior of the two-dimensional random-bond three-state Potts model using large-scale Monte Carlo simulations with the Wolff and Swendsen-Wang cluster algorithms. At the disorder-dependent critical temperature, we compute integrated and exponential autocorrelation times and extract the dynamic critical exponent z via finite-size scaling. Critical slowing down is significantly weakened by bond randomness, with the dynamic exponent decreasing from z≈0.54 in the pure system to z≈0.24 at strong disorder. From the finite-size scaling of the Wolff cluster size, we obtain γ/ν≈1.73, where γ and ν are the susceptibility and correlation-length exponents, respectively, consistent with the universality class of the two-dimensional three-state Potts model. These results indicate that bond randomness strongly affects the critical dynamics but leaves the underlying static universality class unchanged. Furthermore, both static and dynamic observables, including the specific heat and the autocorrelation times, show a lack of self-averaging.

arXiv:2610.01176•Physical review. E•Aug 13, 2026•0 citations

Monte Carlo simulation of phase transitions in a two-dimensional random-bond Potts model

S. Chen, Alan M. Ferrenberg, D. P. Landau

Using the ``multihit'' Swendsen-Wang cluster flipping method, we performed extensive Monte Carlo simulations to investigate the critical behavior of the two-dimensional (2D) eight-state random-bond Potts model. We applied finite-size-scaling techniques to extract the critical exponents for two different sets of bond strengths, from which we concluded that the transition is second order with critical exponents for both sets falling into same universality class, that of a 2D Ising model. A variation of the Lee-Kosterlitz method for determining the order of a phase transition was also applied. The double-peaked structure of the specific heat, which was found in some of the bond configurations, was also studied by simulation on periodic arrangements of strong and weak bonds.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1995•105 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

Critical behavior of the two-dimensional random-bond Potts model: A short-time dynamic approach

Jianwei Yin, Bo Zheng, Steffen Trimper

The short-time critical dynamics of the two-dimensional eight-state random-bond Potts model is investigated with large-scale Monte Carlo simulations. Dynamic relaxation starting from a disordered and an ordered state is carefully analyzed. The continuous phase transition induced by disorder is studied, and both the dynamic and static critical exponents are estimated. The static exponent beta/nu shows little dependence on the disorder amplitude r, while the dynamic exponent z and static exponent 1/nu vary with the strength of disorder.

Physical Review E•Nov 29, 2004•16 citations

Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond Eight-State Potts Model

Christophe Chatelain, Bertrand Berche

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 deduce the corresponding critical exponents at the random fixed point using standard finite-size scaling techniques. The scaling laws are suitably satisfied. We can conclusively rule out that the model belongs to the 2D Ising model universality class. The dimensions of the relevant bulk and surface scaling fields are found to be ${y}_{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.849$, ${y}_{t}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.977$, and ${y}_{{h}_{s}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.54$, in contrast to their Ising values $15/8$, $1$, and $1/2$, respectively.

arXiv:cond-mat/9801028•Physical Review Letters•Feb 23, 1998•97 citations

Short-time dynamics and magnetic critical behavior of the two-dimensional random-bond Potts model

He-Ping Ying, Kenji Harada

The critical behavior in the short-time dynamics for the random-bond Potts ferromagnet in two dimensions is investigated by short-time dynamic Monte Carlo simulations. The numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic, which is used to estimate the critical exponents straight theta,beta/nu, and z, for quenched disordered systems from the power-law behavior of the kth moments of magnetization.

arXiv:cond-mat/0001284•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 1, 2000•20 citations
We present an extensive Monte Carlo study of the critical relaxation for the two-dimensional square lattice random-bond Potts model using Swendsen-Wang cluster flipping. The integrated autocorrelation time \ensuremath{\tau} is calculated and the dynamic exponent z is estimated by analyzing the size dependence of \ensuremath{\tau}. We find that z\ensuremath{\approx}0 in agreement with estimates for the two-dimensional Ising model. We also present a study of the size dependence of the dynamic behavior of the pure eight-state Potts model which undergoes a first-order transition. The scaling is describable by the product of an exponential times a power law, a behavior which is quite different from that found in the random-bond case.
We study the dynamic critical behavior of the two-dimensional random-bond three-state Potts model using large-scale Monte Carlo simulations with the Wolff and Swendsen-Wang cluster algorithms. At the disorder-dependent critical temperature, we compute integrated and exponential autocorrelation times and extract the dynamic critical exponent z via finite-size scaling. Critical slowing down is significantly weakened by bond randomness, with the dynamic exponent decreasing from z≈0.54 in the pure system to z≈0.24 at strong disorder. From the finite-size scaling of the Wolff cluster size, we obtain γ/ν≈1.73, where γ and ν are the susceptibility and correlation-length exponents, respectively, consistent with the universality class of the two-dimensional three-state Potts model. These results indicate that bond randomness strongly affects the critical dynamics but leaves the underlying static universality class unchanged. Furthermore, both static and dynamic observables, including the specific heat and the autocorrelation times, show a lack of self-averaging.
Using the ``multihit'' Swendsen-Wang cluster flipping method, we performed extensive Monte Carlo simulations to investigate the critical behavior of the two-dimensional (2D) eight-state random-bond Potts model. We applied finite-size-scaling techniques to extract the critical exponents for two different sets of bond strengths, from which we concluded that the transition is second order with critical exponents for both sets falling into same universality class, that of a 2D Ising model. A variation of the Lee-Kosterlitz method for determining the order of a phase transition was also applied. The double-peaked structure of the specific heat, which was found in some of the bond configurations, was also studied by simulation on periodic arrangements of strong and weak bonds.
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 short-time critical dynamics of the two-dimensional eight-state random-bond Potts model is investigated with large-scale Monte Carlo simulations. Dynamic relaxation starting from a disordered and an ordered state is carefully analyzed. The continuous phase transition induced by disorder is studied, and both the dynamic and static critical exponents are estimated. The static exponent beta/nu shows little dependence on the disorder amplitude r, while the dynamic exponent z and static exponent 1/nu vary with the strength of disorder.
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 deduce the corresponding critical exponents at the random fixed point using standard finite-size scaling techniques. The scaling laws are suitably satisfied. We can conclusively rule out that the model belongs to the 2D Ising model universality class. The dimensions of the relevant bulk and surface scaling fields are found to be yh=1.849{y}_{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.849yh​=1.849, yt=0.977{y}_{t}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.977yt​=0.977, and yhs=0.54{y}_{{h}_{s}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.54yhs​​=0.54, in contrast to their Ising values 15/815/815/8, 111, and 1/21/21/2, respectively.