Critical Droplets and Replica Symmetry Breaking

TL;DR

This paper explores how critical droplets influence the understanding of ground states in spin glasses, linking their properties to the validity of replica symmetry breaking scenarios across different dimensions.

Contribution

It introduces the concept of critical droplets as a key tool to analyze ground states and phase scenarios in the Edwards-Anderson spin glass model.

Findings

Critical droplets determine the stability of ground states.

The distribution of droplet sizes and energies informs phase scenario validity.

Presence of low-energy interfaces correlates with replica symmetry breaking.

Abstract

We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards-Anderson Ising model of a spin glass in arbitrary dimension. Given a specific ground state, suppose the coupling value for a given edge is varied with all other couplings held fixed. Beyond some specific value of the coupling, a droplet will flip leading to a new ground state; we refer to this as the critical droplet for that edge and ground state. We show that the distribution of sizes and energies over all edges for a specific ground state can be used to determine which of the leading scenarios for the spin glass phase is correct. In particular, the existence of low-energy interfaces between incongruent ground states as predicted by replica symmetry breaking is equivalent to the presence of critical droplets whose boundaries comprise a positive fraction of edges in the infinite lattice.