Single replica spin-glass phase detection using field variation and machine learning

TL;DR

This paper introduces a novel single replica method for detecting spin-glass phases by analyzing the field variation experienced by individual spins, combined with machine learning classification to identify different phases.

Contribution

It proposes a new single replica approach using field variation as indicators and develops a machine learning algorithm for phase classification in spin-glass systems.

Findings

Mean and variance of the Spontaneous Configurational Field effectively distinguish phases

The method successfully classifies ferromagnetic, paramagnetic, and mixed phases

Machine learning enhances phase detection accuracy

Abstract

The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the underlying phases of complex systems such as spin-glasses. Regardless of the method used for detection, the intrinsic phase of a system exists whether or not replicas are considered. We introduce a single replica method of spin-glass phase detection using the field's variation experienced by each spin in a system configuration. This method focuses on a single replica with quenched random couplings. Each spin inevitably observes a different field from the others. Our results show that the mean and variance of fields named "Spontaneous Configurational Field" experienced by spins are suitable indicators to explore different ferromagnetic, paramagnetic, and mixed phases. To classify different phases of the system with defined indicators we have developed an algorithm based on machine learning to analyze the desired samples.