Which measures of spin-glass overlaps are informative?

TL;DR

This paper investigates various overlap measures in spin glasses, revealing that common measures are inconclusive due to scale averaging, but the median of sample-dependent integrals may better distinguish thermodynamic states.

Contribution

It introduces the median of sample-dependent P(q) integrals as a promising measure for understanding spin-glass states, addressing limitations of traditional overlap measures.

Findings

Common overlap measures do not distinguish theoretical pictures.

Strong corrections arise from averaging over many scales.

Median of sample-dependent integrals shows potential for thermodynamic insights.

Abstract

The nature of equilibrium states in disordered materials is often studied using an overlap function P(q), the probability of two configurations having similarity q. Exact sampling simulations of a two-dimensional proxy for three-dimensional spin glasses indicate that common measures of P(q) in smaller samples do not decide between theoretical pictures. Strong corrections result from P(q) being an average over many scales, as seen in a toy droplet model. However, the median of the integrals of sample-dependent P(q) curves shows promise for deciding the thermodynamic behavior.