Ultrametricity and clustering of states in spin glasses: A one-dimensional view

TL;DR

This paper uses Monte Carlo simulations on a one-dimensional spin-glass model with tunable interactions to investigate ultrametricity and clustering, revealing signatures of complex state organization across different universality classes.

Contribution

It demonstrates ultrametric and clustering properties in a tunable one-dimensional spin-glass model, bridging mean-field and non-mean-field behaviors.

Findings

Signatures of ultrametricity in large systems across universality classes

Existence of nontrivial connected components in phase space

Clustering analysis confirms complex state organization

Abstract

We present results from Monte Carlo simulations to test for ultrametricity and clustering properties in spin-glass models. By using a one-dimensional Ising spin glass with random power-law interactions where the universality class of the model can be tuned by changing the power-law exponent, we find signatures of ultrametric behavior both in the mean-field and non-mean-field universality classes for large linear system sizes. Furthermore, we confirm the existence of nontrivial connected components in phase space via a clustering analysis of configurations.