Ultrametric probe of the spin-glass state in a field

TL;DR

This study investigates the ultrametric structure of spin-glass phase space under external fields, revealing that ultrametricity persists only in the mean-field regime and is fragile in non-mean-field cases.

Contribution

It provides new insights into the stability of ultrametricity in spin glasses under external fields across different universality classes.

Findings

Ultrametricity exists in zero field for both mean-field and non-mean-field models.

Applying an external field destroys ultrametricity in non-mean-field models.

Ultrametricity persists only in the mean-field regime under external fields.

Abstract

We study the ultrametric structure of phase space of one-dimensional Ising spin glasses with random power-law interaction in an external random field. Although in zero field the model in both the mean-field and non-mean-field universality classes shows an ultrametric signature [Phys. Rev. Lett. 102, 037207 (2009)], when a field is applied ultrametricity seems only present in the mean-field regime. The results for the non-mean field case in an external field agree with data for spin glasses studied within the Migdal-Kadanoff approximation. Our results therefore suggest that the spin-glass state might be fragile to external fields below the upper critical dimension.