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arXiv:cond-mat/9510009 · Physical review. B, Condensed matter

Phase transition in the three-dimensional ±J Ising spin glass

Naoki Kawashima, A. P. Young

Published Jan 1, 1996• 164 citations
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Abstract

We have studied the three-dimensional Ising spin glass with a $\ifmmode\pm\else\textpm\fi{}J$ 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 ${T}_{c}$ with ordering below ${T}_{c}$. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent $\ensuremath{\nu}$ is somewhat higher. Because there may be (unknown) corrections to finite-size scaling, we do not completely rule out the possibility that ${T}_{c}=0$ or that ${T}_{c}$ is finite but with no order below ${T}_{c}$. However, from our data, these possibilities seem less likely.

DOI
10.1103/physrevb.53.r484

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We have studied the three-dimensional Ising spin glass with a \ifmmode±\else\textpm\fiJ\ifmmode\pm\else\textpm\fi{}J\ifmmode±\else\textpm\fiJ 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{T}_{c}Tc​ with ordering below Tc{T}_{c}Tc​. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent \ensuremathν\ensuremath{\nu}\ensuremathν is somewhat higher. Because there may be (unknown) corrections to finite-size scaling, we do not completely rule out the possibility that Tc=0{T}_{c}=0Tc​=0 or that Tc{T}_{c}Tc​ is finite but with no order below Tc{T}_{c}Tc​. However, from our data, these possibilities seem less likely.
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.
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, PL{\mathrm{P}}_{\mathrm{L}}PL​(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 Tc{\mathrm{T}}_{\mathrm{c}}Tc​${=1.2}_{\mathrm{\ensuremath{-}}0.2}^{+0.1}$, 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.
We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D∓J\mp J∓J Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.
It is shown, by means of Monte Carlo simulation and finite size scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a spin glass and a chiral glass ordering develop. The Monte Carlo algorithm, adapted from lattice gauge theory simulations, makes it possible to thermalize lattices of size L = 32, larger than in any previous spin-glass simulation in three dimensions. High accuracy is reached thanks to the use of the Marenostrum supercomputer. The large range of system sizes studied allows us to consider scaling corrections.
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