Determining Energy Barriers by Iterated Optimization: The Two-Dimensional Ising Spin Glass

TL;DR

This paper introduces a hierarchical constrained optimization method to estimate energy barriers in disordered systems, providing the first bounds for the barrier exponent in 2D Ising spin glasses.

Contribution

The paper presents a novel hierarchical optimization approach using combinatorial algorithms to bound energy barriers in spin glasses, a challenging problem in statistical physics.

Findings

Estimated barrier exponent bounds: 0.25 < ψ < 0.54

First non-trivial numerical bounds for 2D Ising spin glass barriers

Method applicable to other disordered systems

Abstract

Energy barriers determine the dynamics in many physical systems like structural glasses, disordered spin systems or proteins. Here we present an approach, which is based on subdividing the configuration space in a hierarchical manner, leading to upper and lower bounds for the energy barrier separating two configurations. The fundamental operation is to perform a constrained energy optimization, where the degree of constraintness increases with the level in the hierarchy. As application, we consider Ising spin glasses, where the energy barrier which needs to be surmounted in order to flip a compact region of spins of linear dimension $L$ are expected to scale as $L^{\psi}$. The exponent $\psi$ is very hard to estimate from experimental and simulation studies. By using the new approach, applying efficient combinatorial matching algorithms, we are able to give the first non-trivial numerical bounds $0.25 < \psi < 0.54$ for the two-dimensional Ising spin glass.