Overlap Distribution of the Three-Dimensional Ising Model

TL;DR

This paper investigates the overlap probability density in the 3D Ising model at criticality using advanced Monte Carlo simulations, revealing detailed tail behavior and interface tension estimates.

Contribution

It provides the first detailed analysis of the overlap distribution at criticality, including tail behavior and interface tension estimates, using multi-overlap Monte Carlo methods.

Findings

Overlap distribution peaks at q=0 at criticality.

Tail behavior of the distribution is controlled up to 500 orders of magnitude.

Interface tension estimates show smoother approach to infinite volume limit.

Abstract

We study the Parisi overlap probability density P_L(q) for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point P_L(q) is peaked around q=0 in contrast with the double peaked magnetic probability density. We give particular attention to the tails of the overlap distribution at the critical point, which we control over up to 500 orders of magnitude by using the multi-overlap MC algorithm. Below the critical temperature interface tension estimates from the overlap probability density are given and their approach to the infinite volume limit appears to be smoother than for estimates from the magnetization.