Search for a transition in the three-dimensional J Ising spin-glass

Abstract

The three-dimensional Ising spin-glass in zero field with nearest-neighbor interactions having ±J distribution is studied by Monte Carlo simulations for samples of linear dimension L with 3≤L≤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≥1.2 are consistent with a conventional phase transition at ${\mathrm{T}}_{\mathrm{c}}$ ${=1.2\mathrm{}}_{\mathrm{-}0.2}^{+0.1\mathrm{}}$, with exponents ν=1.3±0.3 and η=-0.3±0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.