Overlap Interfaces in Hierarchical Spin-Glass models

TL;DR

This paper introduces a new numerical method and theoretical analysis to characterize overlap interfaces in hierarchical spin-glass models, providing insights into the stability of the spin-glass phase at low temperatures.

Contribution

It presents novel theoretical results and a numerical approach for analyzing overlap interfaces and phase stability in hierarchical spin-glass models, validated by simulations.

Findings

Good agreement between numerical results and theoretical predictions

Characterization of the low-temperature phase of hierarchical spin glasses

Evaluation of the cost for overlap interfaces using Replica Symmetry Breaking

Abstract

We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to characterize the low temperature phase of hierarchical spin-glass models. We use the Replica Symmetry Breaking theory to evaluate the cost for an overlap interface, which in these models is particularly simple. A comparison of our results from numerical simulations with the theoretical predictions shows good agreement.