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Journal de Physique Lettres

Three-dimensional Ising spin-glasses and mean-field theory

Nicolas Sourlas

Published Jan 1, 1984• 23 citations
Publisher

Abstract

The results of a simulation of a three-dimensional nearest neighbour Ising spin-glass are presented and compared with mean-field theory predictions. It is found that the order parameter P(q) has a similar behaviour in the short-range coupling and in the infinite-range coupling model.
DOI
10.1051/jphyslet:019840045020096900

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We discuss the results of numerical simulations of two spin-glass models, the infinite range Sherrington–Kirkpatrick (SK) model, and a nearest–neighbor model in three dimensions. The probability distribution PN(q) for the spin glass order parameter q has been evaluated for the SK model below Tc with N, the number of spins, up to 192. It shows the same basic features as the Parisi function dx/dq as expected, but with sizeable finite size corrections. Results for the short-range model show evidence for a finite temperature transition but further work is needed to confirm this.
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We investigate the order-parameter distribution P(q) of the Ising spin glass with nearest-neighbor interactions in four dimensions using Monte Carlo simulations on lattices of linear dimension up to L=6. We find that, below the transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​, the weight at small q seems to saturate to a nonzero value as the size increases, similar to the infinite-range Sherrington-Kirkpatrick model. We discuss our results in the light of recent theoretical predictions for the nature of the spin-glass phase.