A Numerical Study of Ultrametricity in Finite Dimensional Spin Glasses

TL;DR

This paper uses a specialized Monte Carlo method to investigate the ultrametric structure in a 4D Edwards-Anderson spin glass, finding clear ultrametric features in large systems.

Contribution

It demonstrates the emergence of ultrametricity in finite-dimensional spin glasses using a novel constrained Monte Carlo approach.

Findings

Ultrametric structure becomes evident in large volume limits.

Ultrametricity is observed in the overlap of equilibrium configurations.

The study provides numerical evidence supporting ultrametric organization in 4D spin glasses.

Abstract

We use a constrained Monte Carlo technique to analyze ultrametric features of a 4 dimensional Edwards-Anderson spin glass with quenched couplings J=\pm 1. We find that in the large volume limit an ultrametric structure emerges quite clearly in the overlap of typical equilibrium configurations.