Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses

TL;DR

This paper investigates the structure of low-temperature phases in spin glasses, finding evidence of ultrametricity in the mean-field SK model but not in the 3D short-range Ising spin glass, suggesting different underlying phase space organization.

Contribution

It introduces a clustering-based method to analyze ultrametricity and demonstrates its effectiveness in distinguishing between mean-field and finite-dimensional spin glasses.

Findings

Ultrametricity increases with system size in SK model.

Lack of ultrametricity in 3d Ising spin glass.

Mean field solution does not fully describe 3d ISG.

Abstract

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size increases, while for the short-range case our results indicate the opposite, i.e. lack of ultrametricity. Our results are obtained by a recently proposed method that uses clustering to focus on the relevant parts of phase space and reduce finite size effects. Evidence that the mean field solution does not apply in detail to the 3dISG is also found by another method which does not rely on clustering.