Diluted one-dimensional spin glasses with power law decaying interactions

TL;DR

This paper introduces a diluted one-dimensional spin-glass model with power-law decaying interactions, enabling efficient simulation of larger systems to investigate the nature of the spin-glass phase and support replica symmetry breaking.

Contribution

The authors develop a diluted model that reduces computational complexity, allowing large-scale studies of spin-glass behavior across different interaction ranges.

Findings

Evidence supports replica symmetry breaking in the model.

The diluted model accurately captures static and dynamic properties.

Simulation results align with theoretical predictions.

Abstract

We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models. The spin-glass phase is studied in and out of the range of validity of the mean-field approximation in order to discriminate between different theories. Since each variable interacts only with a finite number of others the cost for simulating the model is drastically reduced with respect to the fully connected version and larger sizes can be studied. We find both static and dynamic evidence in favor of the so-called replica symmetry breaking theory.