Absence of replica symmetry breaking in the Edwards-Anderson model near zero temperature

TL;DR

This paper proves that in the Edwards-Anderson model near zero temperature, the ground state is unique and replica symmetry breaking does not occur, due to the concentration of spin overlap at its maximal value.

Contribution

It establishes the absence of replica symmetry breaking in the Edwards-Anderson model near zero temperature for almost all continuous random interactions.

Findings

Ground state is unique in high dimensions.

Excited states with less than maximal overlap have high energy.

Replica symmetry breaking is absent near zero temperature.

Abstract

It is proven that the ground state is unique in the Edwards-Anderson model for almost all continuous random exchange interactions, and any excited state with the overlap less than its maximal value has large energy in dimensions higher than two with probability one. Since the spin overlap is shown to be concentrated at its maximal value in the ground state, replica symmetry breaking does not occur in the Edwards-Anderson model near zero temperature.