Journal of the Physical Society of Japan

Phase Transition of Three-Dimensional Site-Random Ising Model with Short-Range Interactions

Takayuki Shirakura, Fumitaka Matsubara

Published Sep 15, 1993• 9 citations

Abstract

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$\mp J$ 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.

DOI: 10.1143/jpsj.62.3007

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Journal of the Physical Society of Japan

Phase Transition of Three-Dimensional Site-Random Ising Model with Short-Range Interactions

Takayuki Shirakura, Fumitaka Matsubara

Published Sep 15, 1993• 9 citations

Publisher

Abstract

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(\mp 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.

DOI: 10.1143/jpsj.62.3007

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{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.

{\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.