arXiv:cond-mat/0602212 · Physical Review B

Universality in three-dimensional Ising spin glasses: A Monte Carlo study

Helmut G. Katzgraber, Mathias Körner, A. P. Young

Published Jun 23, 2006• 216 citations

Abstract

We study universality in three-dimensional Ising spin glasses by large-scale Monte Carlo simulations of the Edwards-Anderson Ising spin glass for several choices of bond distributions, with particular emphasis on Gaussian and bimodal interactions. A finite-size scaling analysis suggests that three-dimensional Ising spin glasses obey universality.

DOI: 10.1103/physrevb.73.224432

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arXiv:cond-mat/0602212 · Physical Review B

Universality in three-dimensional Ising spin glasses: A Monte Carlo study

Helmut G. Katzgraber, Mathias Körner, A. P. Young

Published Jun 23, 2006• 216 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.73.224432

Related papers

Universality and universal finite-size scaling functions in four-dimensional Ising spin glasses

Thomas Jörg, Helmut G. Katzgraber

arXiv:0803.3339Physical Review BJun 20, 200820 citations

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Martin Hasenbusch B, Andrea Pelissetto C, Ettore Vicari

We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin glass models on cubic lattices of size $L$ : the $\ifmmode\pm\else\textpm\fi{}J$ (Edwards-Anderson) Ising model for two values of the disorder parameter $p$ , $p=0.5$ and $p=0.7$ (up to $L=28$ and $L=20$ , respectively), and the bond-diluted bimodal model for bond-occupation probability ${p}_{b}=0.45$ (up to $L=16$ ). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent $\ensuremath{\omega}$ related to the leading irrelevant operator: $\ensuremath{\omega}=1.0(1)$. Shorter Monte Carlo simulations of the bond-diluted bimodal models at ${p}_{b}=0.7$ and ${p}_{b}=0.35$ (up to $L=10$ ) and of the Ising spin glass model with Gaussian bond distribution (up to $L=8$ ) also support the existence of a unique Ising spin glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents. We obtain $\ensuremath{\nu}=2.45(15)$ and $\ensuremath{\eta}=\ensuremath{-}0.375(10)$.We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin glass models on cubic lattices of size $L$: the $\ifmmode\pm\else\textpm\fi{}J$ (Edwards-Anderson) Ising model for two values of the disorder parameter $p$, $p=0.5$ and $p=0.7$ (up to $L=28$ and $L=20$, respectively), and the bond-diluted bimodal model for bond-occupation probability ${p}_{b}=0.45$ (up to $L=16$). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent $\ensuremath{\omega}$ related to the leading irrelevant operator: $\ensuremath{\omega}=1.0(1)$. Shorter Monte Carlo simulations of the bond-diluted bimodal models at ${p}_{b}=0.7$ and ${p}_{b}=0.35$ (up to $L=10$) and of the Ising spin glass model with Gaussian bond distribution (up to $L=8$) also support the existence of a unique Ising spin glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents. We obtain $\ensuremath{\nu}=2.45(15)$ and $\ensuremath{\eta}=\ensuremath{-}0.375(10)$.

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We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the universal finite-size scaling (FSS) functions and the critical exponents with high statistical accuracy. We observe small corrections to scaling for the measured observables. The critical quantities and the FSS functions indicate clearly that the bond-diluted model for dilutions above the critical dilution ${p}^{*}$ , at which a spin glass (SG) phase appears, lies in the same universality class as the 3D undiluted EA model with binary interactions. A comparison with the FSS functions of the 3D site-diluted EA model with Gaussian interactions at a site occupation of 62.5% gives very strong evidence for the universality of the SG transition in the 3D EA model.We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the universal finite-size scaling (FSS) functions and the critical exponents with high statistical accuracy. We observe small corrections to scaling for the measured observables. The critical quantities and the FSS functions indicate clearly that the bond-diluted model for dilutions above the critical dilution ${p}^{*}$, at which a spin glass (SG) phase appears, lies in the same universality class as the 3D undiluted EA model with binary interactions. A comparison with the FSS functions of the 3D site-diluted EA model with Gaussian interactions at a site occupation of 62.5% gives very strong evidence for the universality of the SG transition in the 3D EA model.

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We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity v (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain z=5.85(9) for bimodal couplings distribution and z=6.00(10) for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain z=5.93±0.07 for generic 3D Ising spin glasses.We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity v (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain z=5.85(9) for bimodal couplings distribution and z=6.00(10) for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain z=5.93±0.07 for generic 3D Ising spin glasses.

arXiv:1411.6745Physical Review EAug 19, 201525 citations

We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin glass models on cubic lattices of size

L

: the $\ifmmode\pm\else\textpm\fi{}J$ (Edwards-Anderson) Ising model for two values of the disorder parameter

p

p=0.5

and

p=0.7

(up to

L=28

and

L=20

, respectively), and the bond-diluted bimodal model for bond-occupation probability

{p}_{b}=0.45

(up to

L=16

). The finite-size behavior of the quartic cumulants at the critical point allows us to check very accurately that these models belong to the same universality class. Moreover, it allows us to estimate the scaling-correction exponent $\ensuremath{\omega}$ related to the leading irrelevant operator: $\ensuremath{\omega}=1.0(1)$. Shorter Monte Carlo simulations of the bond-diluted bimodal models at

{p}_{b}=0.7

and

{p}_{b}=0.35

(up to

L=10

) and of the Ising spin glass model with Gaussian bond distribution (up to

L=8

) also support the existence of a unique Ising spin glass universality class. A careful finite-size analysis of the Monte Carlo data which takes into account the analytic and the nonanalytic corrections to scaling allows us to obtain precise and reliable estimates of the critical exponents. We obtain $\ensuremath{\nu}=2.45(15)$ and $\ensuremath{\eta}=\ensuremath{-}0.375(10)$.

{p}^{*}

, at which a spin glass (SG) phase appears, lies in the same universality class as the 3D undiluted EA model with binary interactions. A comparison with the FSS functions of the 3D site-diluted EA model with Gaussian interactions at a site occupation of 62.5% gives very strong evidence for the universality of the SG transition in the 3D EA model.