Network of inherent structures in spin glasses: scaling and scale-free distributions

TL;DR

This paper investigates the topological properties of networks formed by local minima in spin glasses, revealing scale-free degree distributions and a growth of characteristic length scales with barrier height.

Contribution

It introduces a novel analysis of inherent structure networks in spin glasses, highlighting scale-free distributions and droplet-based interpretations.

Findings

Degree distribution exhibits a scale-free tail.

Characteristic length scale grows with barrier height.

Network topology reflects droplet clustering.

Abstract

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest descent dynamics, determining for each disorder sample the transition links appearing within a given barrier height. We find that differences between linked inherent structures are typically associated with local clusters of spins; we interpret this within a framework based on droplets in which the characteristic ``length scale'' grows with the barrier height. We also consider the network connectivity and the degrees of its nodes. Interestingly, for spin glasses based on random graphs, the degree distribution of the network of inherent structures exhibits a non-trivial scale-free tail.