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

The recent interpretation of Parisi's order-parameter function $q(x)$ 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 $q(x)$ are reproduced, in particular q(x)∝x as x→0 and q^'(x)=0 at q=qₘₐₓ, the largest value. Finite-size effects prevent one from establishing with certainty whether there is a "plateau," i.e., q^'(x)=0 for a range of x.