New Insights from One-Dimensional Spin Glasses

TL;DR

This paper investigates one-dimensional spin glasses with tunable power-law interactions to understand the applicability of mean-field replica symmetry breaking predictions to short-range systems, exploring phase existence, ultrametricity, and algorithm performance.

Contribution

It introduces a versatile one-dimensional spin glass model that bridges mean-field and short-range universality classes, enabling large-scale simulations and testing theoretical predictions.

Findings

Existence of spin-glass phase in external field analyzed

Ultrametricity in short-range spin glasses discussed

Model serves as a test-bed for optimization algorithms

Abstract

The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial analysis. Thus it is of paramount importance to understand which predictions of the mean-field solution apply to non-mean-field systems, such as realistic short-range spin-glass models. The one-dimensional spin glass with random power-law interactions promises to be an ideal test-bed to answer this question: Not only can large system sizes-which are usually a shortcoming in simulations of high-dimensional short-range system-be studied, by tuning the power-law exponent of the interactions the universality class of the model can be continuously tuned from the mean-field to the short-range universality class. We present details of the model, as well as recent applications to some questions of the physics of spin glasses. First, we study the existence of a spin-glass state in an external field. In addition, we discuss the existence of ultrametricity in short-range spin glasses. Finally, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms.