Spin glasses and algorithm benchmarks: A one-dimensional view

TL;DR

This paper explores a one-dimensional long-range spin-glass model with tunable interactions, serving as a versatile tool for studying high-dimensional spin glasses and benchmarking optimization algorithms.

Contribution

It introduces a one-dimensional model with adjustable power-law interactions that simulates high-dimensional spin glasses and aids in testing algorithms.

Findings

Model allows tuning effective dimension via interaction range.

Facilitates study of complex phenomena like ultrametricity and chaos.

Serves as a benchmark for optimization algorithms.

Abstract

Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore large-scale numerical simulations are the tool of choice. Concepts and algorithms derived from the study of spin glasses have been applied to diverse fields in computer science and physics. In this work a one-dimensional long-range spin-glass model with power-law interactions is discussed. The model has the advantage over conventional systems in that by tuning the power-law exponent of the interactions the effective space dimension can be changed thus effectively allowing the study of large high-dimensional spin-glass systems to address questions as diverse as the existence of an Almeida-Thouless line, ultrametricity and chaos in short range spin glasses. Furthermore, because the range of interactions can be changed, the model is a formidable test-bed for optimization algorithms.