Ground State Stability and the Nature of the Spin Glass Phase

TL;DR

This paper investigates the stability of spin glass ground states at low temperatures by analyzing their response to perturbations, connecting various theoretical scenarios with geometric and energetic properties of excitations.

Contribution

It introduces sigma-criticality as a new measure to distinguish between different spin glass phases based on ground state sensitivity to bond perturbations.

Findings

Different spin glass scenarios correspond to distinct critical droplet geometries.

Sigma-criticality effectively characterizes ground state stability and phase distinctions.

Conditions for multiple incongruent ground states are identified.

Abstract

We propose an approach toward understanding the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. After reviewing the concepts of flexibility, critical droplet, and related quantities for both finite- and infinite-volume ground states, we study some of their properties and review three models in which these quantities are partially or fully understood. We also review a recent result showing the connection between our approach and that of disorder chaos. We then view four proposed scenarios for the low-temperature spin glass phase -- replica symmetry breaking, scaling-droplet, TNT and chaotic pairs -- through the lens of the predictions of each scenario for the lowest energy large-lengthscale excitations above the ground state. Using a new concept called sigma-criticality, which quantifies the sensitivity of ground states to single-bond coupling variations, we show that each of these four pictures can be identified with different critical droplet geometries and energies. We also investigate necessary and sufficient conditions for the existence of multiple incongruent ground states.