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/9506117 · Physical review. B, Condensed matter

Weak universality in the two-dimensional randomly disordered three-state Potts ferromagnet

Jae-Kwon Kim

Published Feb 1, 1996• 20 citations
arXivHTMLPDF

Abstract

For the two-dimensional randomly disordered three-state Potts ferromagnet, we find numerically that the critical exponents of the correlation length \ensuremath{\nu}, magnetic susceptibility \ensuremath{\gamma}, and magnetization \ensuremath{\beta} increase continuously with the strength of disorder, while the ratios \ensuremath{\gamma}/\ensuremath{\nu} and \ensuremath{\beta}/\ensuremath{\nu} remain unchanged (thus verifying the hyperscaling relation \ensuremath{\gamma}+2\ensuremath{\beta}=D\ensuremath{\nu}). Our finding indicates the presence of a certain universal feature valid in any disordered ferromagnet, which can be explained by the weak universality concept. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.3388

Related papers

Weak Universality in the Disordered Two-Dimensional Antiferromagnetic Potts Model on a Triangular Lattice

Albert Babaevich Babaev, Akai Kurbanovich Murtazaev

The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality $$\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = d$$ . Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.

Journal of Experimental and Theoretical Physics Letters•May 1, 2018•5 citations

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

Computer simulation of the critical behavior of highly diluted low-dimensional antiferromagnetic systems on a triangular lattice

Albert Babaevich Babaev, Akai Kurbanovich Murtazaev

A computer simulation of the critical behavior of a two-dimensional highly diluted 3-state antiferromagnetic Potts model on a triangular lattice is performed. The calculations are done for systems with periodic boundary conditions at spin concentrations p equal to 0.70 and 0.65. Systems with linear dimensions L×L = N, L = 20–144 are considered. Based on the theory of finite-dimensional scaling, the static critical exponents of heat capacity α, susceptibility γ, order parameter β, and critical index ν for the correlation radius are calculated. It is numerically shown that the calculated critical exponents vary with changes in the spin concentration p, while the ratios β/ν and γ/ν remain unchanged within error, showing a weak universality of the critical behavior of disordered systems.

Low Temperature Physics•Dec 1, 2018•2 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

Critical dynamics of the two-dimensional random-bond Potts model with nonequilibrium Monte Carlo simulations

Shuangli Fan, Fan Zhong

We study two-dimensional q -state random-bond Potts models for both q=8 and q=5 with a linearly varying temperature. By applying a successive Monte Carlo renormalization group procedure, both the static and dynamic critical exponents are obtained for randomness amplitudes (the strong to weak coupling ratio) of r_{0}=3 , 10, 15, and 20. The correlation length exponent nu increases with disorder from less than to larger than unity and this variation is justified by the good collapse of the specific heat near the critical region. The specific heat exponent is obtained by the usual hyperscaling relation alpha=2-dnu and thus indicates no possibility of the activated dynamic scaling. Both r_{0} and q have effects on the critical dynamics of the disordered systems, which can be seen from variations of the rate exponent, the hysteresis exponent, and the dynamic critical exponent. Implications of these results are discussed.

Physical Review E•Jan 22, 2009•8 citations

Griffiths singularity in the two dimensional random bond disordered Ising ferromagnet

Jae-Kwon Kim

For the two dimensional random bond disordered Ising ferromagnet, we measured bulk data of the magnetic susceptibility ($χ$) and correlation length ($ξ$) up to $ξ\simeq 536$, with the use of a novel finite size scaling Monte Carlo technique. Our data are exclusively consistent with normal power-law critical behaviors with only one singular point at criticality, disproving the existence of Griffiths singularity even in an extremely deep scaling region. The critical exponents of $χ$ and $ξ$ increase continuously with the strength of disorder.

arXiv:cond-mat/9502053•Feb 13, 1995•0 citations
For the two-dimensional randomly disordered three-state Potts ferromagnet, we find numerically that the critical exponents of the correlation length \ensuremath{\nu}, magnetic susceptibility \ensuremath{\gamma}, and magnetization \ensuremath{\beta} increase continuously with the strength of disorder, while the ratios \ensuremath{\gamma}/\ensuremath{\nu} and \ensuremath{\beta}/\ensuremath{\nu} remain unchanged (thus verifying the hyperscaling relation \ensuremath{\gamma}+2\ensuremath{\beta}=D\ensuremath{\nu}). Our finding indicates the presence of a certain universal feature valid in any disordered ferromagnet, which can be explained by the weak universality concept. \textcopyright{} 1996 The American Physical Society.
The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality 2βν+γν=d\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = dν2β​+νγ​=d . Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.
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.
A computer simulation of the critical behavior of a two-dimensional highly diluted 3-state antiferromagnetic Potts model on a triangular lattice is performed. The calculations are done for systems with periodic boundary conditions at spin concentrations p equal to 0.70 and 0.65. Systems with linear dimensions L×L = N, L = 20–144 are considered. Based on the theory of finite-dimensional scaling, the static critical exponents of heat capacity α, susceptibility γ, order parameter β, and critical index ν for the correlation radius are calculated. It is numerically shown that the calculated critical exponents vary with changes in the spin concentration p, while the ratios β/ν and γ/ν remain unchanged within error, showing a weak universality of the critical behavior of disordered systems.
We study two-dimensional q -state random-bond Potts models for both q=8 and q=5 with a linearly varying temperature. By applying a successive Monte Carlo renormalization group procedure, both the static and dynamic critical exponents are obtained for randomness amplitudes (the strong to weak coupling ratio) of r_{0}=3 , 10, 15, and 20. The correlation length exponent nu increases with disorder from less than to larger than unity and this variation is justified by the good collapse of the specific heat near the critical region. The specific heat exponent is obtained by the usual hyperscaling relation alpha=2-dnu and thus indicates no possibility of the activated dynamic scaling. Both r_{0} and q have effects on the critical dynamics of the disordered systems, which can be seen from variations of the rate exponent, the hysteresis exponent, and the dynamic critical exponent. Implications of these results are discussed.
For the two dimensional random bond disordered Ising ferromagnet, we measured bulk data of the magnetic susceptibility (χχχ) and correlation length (ξξξ) up to ξ≃536ξ\simeq 536ξ≃536, with the use of a novel finite size scaling Monte Carlo technique. Our data are exclusively consistent with normal power-law critical behaviors with only one singular point at criticality, disproving the existence of Griffiths singularity even in an extremely deep scaling region. The critical exponents of χχχ and ξξξ increase continuously with the strength of disorder.