Efficient algorithms for computing ground states of the 2D random-field Ising model

TL;DR

This paper explores efficient graph-cut algorithms to compute exact ground states of the 2D random-field Ising model, analyzing their performance across different lattice types and disorder strengths.

Contribution

It introduces and compares two minimum-cut--maximum-flow algorithms for exact ground-state calculations in the 2D RFIM on square and triangular lattices.

Findings

Algorithms successfully compute ground states across phase boundary

Push-relabel method shows higher efficiency than augmenting-path

Results facilitate better understanding of critical behavior in RFIM

Abstract

We investigate the application of graph-cut methods for the study of the critical behaviour of the two-dimensional random-field Ising model. We focus on exact ground-state calculations, crossing the phase boundary of the model at zero temperature and varying the disorder strength. For this purpose we employ two different minimum-cut--maximum-flow algorithms, one of augmenting-path and another of push-relabel style. We implement these approaches for the square and triangular lattice problems and compare their computational efficiency.