Degeneracy Algorithm for Random Magnets

TL;DR

This paper introduces an exact algorithm based on residual graphs to find all ground states of random magnets, enhancing understanding of their degeneracy and related physical systems.

Contribution

The paper presents a novel algorithm that accurately identifies all minimum cuts, and thus the ground state degeneracy, in random magnet models using max-flow/min-cut mapping.

Findings

Algorithm is proven exact for all minimum cuts.

Applicable to RFIM, DAFF, and interfaces in random bond magnets.

Improves analysis of ground state properties in disordered magnetic systems.

Abstract

It has been known for a long time that the ground state problem of random magnets, e.g. random field Ising model (RFIM), can be mapped onto the max-flow/min-cut problem of transportation networks. I build on this approach, relying on the concept of residual graph, and design an algorithm that I prove to be exact for finding all the minimum cuts, i.e. the ground state degeneracy of these systems. I demonstrate that this algorithm is also relevant for the study of the ground state properties of the dilute Ising antiferromagnet in a constant field (DAFF) and interfaces in random bond magnets.