Physical Review Letters

Critical behavior of three-dimensional Ising spin-glass model

Andrew T. Ogielski, I. Morgenstern

Published Mar 4, 1985• 362 citations

Abstract

First results of massive Monte Carlo simulations of the d=3 Ising spin-glass with \ifmmode\pm\else\textpm\fi{}J bond distribution, performed on a fast special purpose computer, are presented. A qualitative change in the behavior of the system and best fits for the spin-glass correlation length and relaxation time favor equilibrium phase transition at ${\mathrm{T}}_{\mathrm{c}}$/J\ensuremath{\approxeq}1.2. .AE

DOI: 10.1103/physrevlett.54.928

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Physical Review Letters

Critical behavior of three-dimensional Ising spin-glass model

Andrew T. Ogielski, I. Morgenstern

Published Mar 4, 1985• 362 citations

Publisher

Abstract

{\mathrm{T}}_{\mathrm{c}}

/J\ensuremath{\approxeq}1.2. .AE

DOI: 10.1103/physrevlett.54.928

Related papers

Critical behavior of three-dimensional Ising model of spin glass (invited)

Andrew T. Ogielski, I. Morgenstern

First results of massive Monte Carlo simulations of the d=3 Ising spin glass with ± J bond distribution, performed on a fast special purpose computer, are discussed. Equilibrium static and dynamic correlation functions have been recorded for temperatures T/J=1.10 to 2.00. A qualitative change in the behavior of the system, and the best fits for the spin glass correlation length and relaxation time favor a continuous phase transition at Tc/J≊1.20±0.05. We find no evidence for the Tc=0 freezing picture.First results of massive Monte Carlo simulations of the d=3 Ising spin glass with ± J bond distribution, performed on a fast special purpose computer, are discussed. Equilibrium static and dynamic correlation functions have been recorded for temperatures T/J=1.10 to 2.00. A qualitative change in the behavior of the system, and the best fits for the spin glass correlation length and relaxation time favor a continuous phase transition at Tc/J≊1.20±0.05. We find no evidence for the Tc=0 freezing picture.

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Andrew T. Ogielski, I. Morgenstern

Jan 1, 19854 citations

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R. N. Bhatt, A. P. Young

The three-dimensional Ising spin-glass in zero field with nearest-neighbor interactions having \ifmmode\pm\else\textpm\fi{}J distribution is studied by Monte Carlo simulations for samples of linear dimension L with 3\ensuremath{\le}L\ensuremath{\le}20. Results for the probability distribution, ${\mathrm{P}}_{\mathrm{L}}$ (q), of the spin-glass order parameter are analyzed by finite-size scaling. Data for T\ensuremath{\ge}1.2 are consistent with a conventional phase transition at ${\mathrm{T}}_{\mathrm{c}}$ ${=1.2}_{\mathrm{\ensuremath{-}}0.2}^{+0.1}$, with exponents \ensuremath{\nu}=1.3\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\eta}=-0.3\ifmmode\pm\else\textpm\fi{}0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.The three-dimensional Ising spin-glass in zero field with nearest-neighbor interactions having \ifmmode\pm\else\textpm\fi{}J distribution is studied by Monte Carlo simulations for samples of linear dimension L with 3\ensuremath{\le}L\ensuremath{\le}20. Results for the probability distribution, ${\mathrm{P}}_{\mathrm{L}}$(q), of the spin-glass order parameter are analyzed by finite-size scaling. Data for T\ensuremath{\ge}1.2 are consistent with a conventional phase transition at ${\mathrm{T}}_{\mathrm{c}}$${=1.2}_{\mathrm{\ensuremath{-}}0.2}^{+0.1}$, with exponents \ensuremath{\nu}=1.3\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\eta}=-0.3\ifmmode\pm\else\textpm\fi{}0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.

Physical Review LettersMar 4, 1985392 citations

Universality in three-dimensional Ising spin glasses: Nonequilibrium dynamics from Monte Carlo simulations

FEDERICO J. ROMÁ

arXiv:1007.4780Physical Review BDec 13, 20108 citations

{\mathrm{T}}_{\mathrm{c}}

/J\ensuremath{\approxeq}1.2. .AE

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 $\ensuremath{\eta}=\ensuremath{-}0.375(10)$.

{\mathrm{P}}_{\mathrm{L}}

(q), of the spin-glass order parameter are analyzed by finite-size scaling. Data for T\ensuremath{\ge}1.2 are consistent with a conventional phase transition at

{\mathrm{T}}_{\mathrm{c}}

${=1.2}_{\mathrm{\ensuremath{-}}0.2}^{+0.1}$, with exponents \ensuremath{\nu}=1.3\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\eta}=-0.3\ifmmode\pm\else\textpm\fi{}0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.