Multi-Overlap Simulations of the $3d$ Edwards-Anderson Ising Spin Glass

TL;DR

This paper introduces a new simulation method for 3D Edwards-Anderson Ising spin glasses that enables detailed analysis of the overlap distribution and tunneling barriers, supporting the validity of Parisi mean field theory in three dimensions.

Contribution

A novel multi-overlap simulation technique for spin glasses that allows comprehensive analysis of the overlap parameter distribution and tunneling barriers in 3D systems.

Findings

Reliable results on spin glass tunneling barriers.

Support for Parisi mean field theory validity in 3D.

Feasibility of broad overlap distribution simulations.

Abstract

We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for the entire $q$-range (multi-overlap) follow by re-weighting. We demonstrate the feasibility of the approach by studying the $3d$ Edwards-Anderson Ising ($J_{ik}=\pm 1$) spin glass in the broken phase ($\beta=1$). For the first time it becomes possible to obtain reliable results about spin glass tunneling barriers. In addition, as do some earlier numerical studies, our results support that Parisi mean field theory is valid down to $3d$.