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

International Journal of Modern Physics C

EXTENDED SCALING SCHEME FOR CRITICALLY DIVERGENT QUANTITIES AND CRITICAL EXPONENTS OF AN ISING SPIN GLASS

Koji Hukushima, Ian A. Campbell, Hajime Takayama

Published Sep 1, 2009• 2 citations
Publisher

Abstract

A long-standing issue in a three-dimensional Ising spin glass (3DISG) is to settle the critical exponents. Numerical simulations and a conventional finite-size-scaling analysis have given controversial estimates, in particular, for the value of thermal exponent ν. Here a recently proposed extended scaling scheme is reviewed and illustrated for the canonical two-dimensional Ising ferromagnet. By applying the extended scaling to our extensive Monte Carlo data for 3DISG, consistent estimates of critical parameters are obtained in contrast to previous analyses.

DOI
10.1142/s0129183109014382

Related papers

Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses

Ian A. Campbell, Koji Hukushima, Hajime Takayama

From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scheme involving a set of scaling formulas which expresses to leading order the temperature (T) and the system size (L) dependences of thermodynamic observables over a much wider range of T than the corresponding one in the conventional scaling scheme. The extended scaling, illustrated by data on the canonical 2d ferromagnet and on the 3d bimodal Ising spin glass, leads to consistency in the estimates of critical parameters obtained from scaling analyses for different observables.

arXiv:cond-mat/0603453•Physical Review Letters•Sep 14, 2006•58 citations

The critical behavior of 3D Ising spin glass models: universality and scaling corrections

Martin Hasenbusch, Andrea Pelissetto, Ettore Vicari

We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin glass models: the ± J Ising model for two values of the disorder parameter p , p = 1/2 and 0.7, and the bond-diluted ± J model for bond-occupation probability p b = 0.45. A finite-size scaling analysis of the quartic cumulants at the critical point shows conclusively that these models belong to the same universality class and allows us to estimate the scaling-correction exponent ω related to the leading irrelevant operator, ω = 1.0(1). We also determine the critical exponents ν and η. Taking into account the scaling corrections, we obtain ν = 2.53(8) and η = −0.384(9).

arXiv:0710.1980•Journal of Statistical Mechanics Theory and Experiment•Feb 1, 2008•50 citations

Ising spin glasses: Corrections to finite size scaling, freezing temperatures, and critical exponents

Pierre‐Olivier Mari, Ian A. Campbell

We compare simulation data from different sources on two canonical three-dimensional Ising spin glasses (ISGs): the binomial $\ifmmode\pm\else\textpm\fi{}J$ near-neighbor interaction ISG and the Gaussian interaction ISG. We allow for the possibility of corrections to finite size scaling and estimate the correction exponent w. Consistent estimates for the critical temperatures ${T}_{g}$ and for the critical exponents for each system are obtained. The data strongly indicate that critical exponents in the two systems are significantly different from each other. These results thus confirm a breakdown of standard universality rules in Ising spin glasses.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 1, 1999•29 citations

The critical exponents of the two-dimensional Ising spin glass revisited: exact ground-state calculations and Monte Carlo simulations

Heiko Rieger, Ludger Santen, Ulrich Blasum +3 more

The critical exponents for of the two-dimensional Ising spin-glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to L = 50 and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent , for the magnetic exponent and for the chaos exponent . From Monte Carlo simulations we get the thermal exponent . The scaling prediction is fulfilled within the error bars, whereas there is a disagreement with the relation .

arXiv:cond-mat/9604050•Journal of Physics A Mathematical and General•Jul 21, 1996•107 citations

RECENT DEVELOPMENTS IN ISING SPIN GLASSES

A. P. Young, Naoki Kawashima

We have studied the three-dimensional Ising spin glass with a ± J distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite size scaling analysis shows quite strong evidence for a finite transition temperature, Tc, with ordering below Tc. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, ν, is somewhat higher. Because there may be (unknown) corrections to finite size scaling, we do not completely rule out the possibility that Tc = 0 or that Tc is finite but with no order below Tc. However, from our data, these possibilities seem less likely.

International Journal of Modern Physics C•Jun 1, 1996•3 citations

CRITICAL EXPONENTS OF THE 3-D ISING MODEL

Rajan Gupta, Pablo Tamayo

We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on 643, 1283, and 2563 simple cubic lattices. Our MCRG estimates are [Formula: see text] and ν = 0.625(1). The FSS results for Kc are consistent with those from MCRG but the value of ν is not. Our best estimate η = 0.025(6) covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate ω ≈ 0.7 for the correction-to-scaling exponent. We also present results for the renormalized coupling gR along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.

arXiv:cond-mat/9601048•International Journal of Modern Physics C•Jun 1, 1996•38 citations
A long-standing issue in a three-dimensional Ising spin glass (3DISG) is to settle the critical exponents. Numerical simulations and a conventional finite-size-scaling analysis have given controversial estimates, in particular, for the value of thermal exponent ν. Here a recently proposed extended scaling scheme is reviewed and illustrated for the canonical two-dimensional Ising ferromagnet. By applying the extended scaling to our extensive Monte Carlo data for 3DISG, consistent estimates of critical parameters are obtained in contrast to previous analyses.
From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scheme involving a set of scaling formulas which expresses to leading order the temperature (T) and the system size (L) dependences of thermodynamic observables over a much wider range of T than the corresponding one in the conventional scaling scheme. The extended scaling, illustrated by data on the canonical 2d ferromagnet and on the 3d bimodal Ising spin glass, leads to consistency in the estimates of critical parameters obtained from scaling analyses for different observables.
We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin glass models: the ± J Ising model for two values of the disorder parameter p , p = 1/2 and 0.7, and the bond-diluted ± J model for bond-occupation probability p b = 0.45. A finite-size scaling analysis of the quartic cumulants at the critical point shows conclusively that these models belong to the same universality class and allows us to estimate the scaling-correction exponent ω related to the leading irrelevant operator, ω = 1.0(1). We also determine the critical exponents ν and η. Taking into account the scaling corrections, we obtain ν = 2.53(8) and η = −0.384(9).
We compare simulation data from different sources on two canonical three-dimensional Ising spin glasses (ISGs): the binomial $\ifmmode\pm\else\textpm\fi{}J$ near-neighbor interaction ISG and the Gaussian interaction ISG. We allow for the possibility of corrections to finite size scaling and estimate the correction exponent w. Consistent estimates for the critical temperatures Tg{T}_{g}Tg​ and for the critical exponents for each system are obtained. The data strongly indicate that critical exponents in the two systems are significantly different from each other. These results thus confirm a breakdown of standard universality rules in Ising spin glasses.
The critical exponents for of the two-dimensional Ising spin-glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to L = 50 and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent , for the magnetic exponent and for the chaos exponent . From Monte Carlo simulations we get the thermal exponent . The scaling prediction is fulfilled within the error bars, whereas there is a disagreement with the relation .
We have studied the three-dimensional Ising spin glass with a ± J distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite size scaling analysis shows quite strong evidence for a finite transition temperature, Tc, with ordering below Tc. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, ν, is somewhat higher. Because there may be (unknown) corrections to finite size scaling, we do not completely rule out the possibility that Tc = 0 or that Tc is finite but with no order below Tc. However, from our data, these possibilities seem less likely.
We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on 643, 1283, and 2563 simple cubic lattices. Our MCRG estimates are [Formula: see text] and ν = 0.625(1). The FSS results for Kc are consistent with those from MCRG but the value of ν is not. Our best estimate η = 0.025(6) covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate ω ≈ 0.7 for the correction-to-scaling exponent. We also present results for the renormalized coupling gR along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.