Direct Determination of the Probability Distribution for the Spin-Glass Order Parameter

Abstract

The recent interpretation of Parisi's order-parameter function $q\left(x\right)\mathrm{}$ in terms of a probability distribution for the overlap between magnetizations in different phases is investigated by Monte Carlo computer simulation for the infinite-range Ising spin-glass model. The main features of the solution for $q\left(x\right)\mathrm{}$ are reproduced, in particular $q\mathrm{}\left(x\right)\mathrm{}\propto x$ as $x\to 0$ and $q^{\prime }\mathrm{}\left(x\right)=0\mathrm{}$ at $q=q_{max}$, the largest value. Finite-size effects prevent one from establishing with certainty whether there is a "plateau," i.e., $q^{\prime }\mathrm{}\left(x\right)=0\mathrm{}$ for a range of $x$.