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

arXiv:cond-mat/9712095 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Softening of the phase transition in a two-dimensional Potts model under quenched bond randomness

Fatih Yaşar, Y. Gündüç, Tarık Çelik

Published Oct 1, 1998• 15 citations
arXivHTMLPDF

Abstract

We have simulated, by using a cluster algorithm, the $q=8$ state Potts model in two dimensions with a varying amount of quenched bond randomness. We have shown that there exists a finite size-dependent threshold value of the introduced quenched bond randomness for rounding the first-order phase transition and that this threshold value becomes smaller as the system size increases.

DOI
10.1103/physreve.58.4210

Related papers

STUDY OF AUTOCORRELATION TIMES IN 2D POTTS MODEL UNDER QUENCHED BOND RANDOMNESS

Fatih Yaşar, Y. Gündüç, Tarık Çelik

The q = 8 state Potts model with varying amount of quenched bond randomness is simulated in two dimensions by using a cluster algorithm. It is shown that, by monitoring the autocorrelation times, one can trace down the threshold value of the introduced quenched bond randomness for the rounding of the first-order phase transition.

International Journal of Modern Physics C•Jun 1, 2000•0 citations

Softening of first-order transition in three-dimensions by quenched disorder

Christophe Chatelain, Bertrand Berche, Wolfhard Janke E +1 more

We study by extensive Monte Carlo simulations the effect of random bond dilution on the phase transition of the three-dimensional four-state Potts model that is known to exhibit a strong first-order transition in the pure case. The phase diagram in the dilution-temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes. In the strongly disordered regime, numerical evidence for softening to a second-order transition induced by randomness is given. Here a large-scale finite-size scaling analysis, made difficult due to strong crossover effects presumably caused by the percolation fixed point, is performed.

arXiv:cond-mat/0103377•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 29, 2001•57 citations

Randomness-induced second-order transition in the two-dimensional eight-state Potts model: A Monte Carlo study

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

We have studied the effect of quenched, bond randomness on the nature of the phase transition in the two-dimensional eight-state Potts model. Through extensive Monte Carlo simulations, we confirm that the phase transition changes from first order to second order. A finite-size-scaling analysis of several thermodynamic quantities strongly suggests that the critical exponents fall into the universality class of the two-dimensional Ising model.

Physical Review Letters•Aug 24, 1992•116 citations

THE STUDY OF QUENCHED BOND RANDOMNESS BY WANG–LANDAU ALGORITHM

Fatih Yaşar

Monte Carlo simulations using the recently proposed Wang–Landau algorithm are performed to the q = 8 state Potts model in two dimension with various degrees of randomness. We systematically studied the effect of quenched bond randomness to system which has first-order phase transition. All simulations and measurements were done from pure case r = 1 to r = 0.4. Physical quantities such as energy density and ground-state entropy were evaluated at all temperatures. We have also obtained probability distributions of energy to monitor softening of transitions. It appears quite feasible to simulate spin systems with quenched bond randomness by Wang–Landau algorithm.

International Journal of Modern Physics C•Jul 1, 2007•0 citations

Critical Behavior of Random-Bond Potts Models

John Cardy, Jesper Lykke Jacobsen

The effect of quenched impurities on systems undergoing first-order phase transitions is studied within the framework of the $q$-state Potts model. For large $q$ a mapping to the random-field Ising model explains the absence of any latent heat in 2D, and suggests that for $d>2$ such systems exhibit a tricritical point with an exponent $\ensuremath{\nu}$ related to those of the random-field model by $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\nu}}_{\mathrm{RF}}/(2\ensuremath{-}{\ensuremath{\alpha}}_{\mathrm{RF}}\ensuremath{-}{\ensuremath{\beta}}_{\mathrm{RF}})$. In 2D we analyze the model using finite-size scaling and conformal invariance, and find a continuous transition with a ratio $\ensuremath{\beta}/\ensuremath{\nu}$ which varies continuously with $q$, and a weakly varying exponent $\ensuremath{\nu}\ensuremath{\approx}1$. We find strong evidence for the multiscaling of the correlation functions.

arXiv:cond-mat/9705038•Physical Review Letters•Nov 24, 1997•169 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
We have simulated, by using a cluster algorithm, the q=8q=8q=8 state Potts model in two dimensions with a varying amount of quenched bond randomness. We have shown that there exists a finite size-dependent threshold value of the introduced quenched bond randomness for rounding the first-order phase transition and that this threshold value becomes smaller as the system size increases.
We study by extensive Monte Carlo simulations the effect of random bond dilution on the phase transition of the three-dimensional four-state Potts model that is known to exhibit a strong first-order transition in the pure case. The phase diagram in the dilution-temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes. In the strongly disordered regime, numerical evidence for softening to a second-order transition induced by randomness is given. Here a large-scale finite-size scaling analysis, made difficult due to strong crossover effects presumably caused by the percolation fixed point, is performed.
Monte Carlo simulations using the recently proposed Wang–Landau algorithm are performed to the q = 8 state Potts model in two dimension with various degrees of randomness. We systematically studied the effect of quenched bond randomness to system which has first-order phase transition. All simulations and measurements were done from pure case r = 1 to r = 0.4. Physical quantities such as energy density and ground-state entropy were evaluated at all temperatures. We have also obtained probability distributions of energy to monitor softening of transitions. It appears quite feasible to simulate spin systems with quenched bond randomness by Wang–Landau algorithm.
The effect of quenched impurities on systems undergoing first-order phase transitions is studied within the framework of the qqq-state Potts model. For large qqq a mapping to the random-field Ising model explains the absence of any latent heat in 2D, and suggests that for d>2d>2d>2 such systems exhibit a tricritical point with an exponent $\ensuremath{\nu}$ related to those of the random-field model by $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\nu}}_{\mathrm{RF}}/(2\ensuremath{-}{\ensuremath{\alpha}}_{\mathrm{RF}}\ensuremath{-}{\ensuremath{\beta}}_{\mathrm{RF}})$. In 2D we analyze the model using finite-size scaling and conformal invariance, and find a continuous transition with a ratio $\ensuremath{\beta}/\ensuremath{\nu}$ which varies continuously with qqq, and a weakly varying exponent $\ensuremath{\nu}\ensuremath{\approx}1$. We find strong evidence for the multiscaling of the correlation functions.
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.