A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model

In this paper we study the fluctuations of the probability distributions of the overlap in mean-field spin glasses in the presence of a magnetic field on the De Almeida–Thouless line. We find that there is a large tail in the left part of the distribution that is dominated by the contributions of rare samples. Different techniques are used to examine the data and to stress different aspects of the contribution of rare samples.