Energy barriers in spin glasses

TL;DR

This paper investigates how energy barriers scale in Ising spin glasses on hierarchical lattices, revealing a universal power-law relation with system size across dimensions, supported by analytical and computational methods.

Contribution

It introduces a method to evaluate lower bounds of energy barriers efficiently and demonstrates their scaling behavior in high-dimensional spin glasses.

Findings

Energy barrier scales as L^{d-1} for all dimensions d

Analytical evaluation of the infinite-dimensional limit

Algorithm remains efficient for large systems

Abstract

For an Ising spin glass on a hierarchical lattice, we show that the energy barrier to be overcome during the flip of a domain of size L scales as L to the power d-1 for all dimensions d. We do this by investigating appropriate lower bounds to the barrier energy, which can be evaluated using an algorithm that remains fast for large system sizes and dimensions. The asymptotic limit of infinite dimensions is evaluated analytically.