Exploring optimization for the random-field Ising model

TL;DR

This paper investigates the optimization of the push-relabel algorithm for efficiently computing exact ground states of the random-field Ising model across different dimensions, providing practical implementation insights.

Contribution

It analyzes various implementations of the push-relabel algorithm, identifies the most efficient version, and offers visualization-based insights for further optimization.

Findings

Identified the fastest push-relabel implementation for RFIM

Provided empirical timing results in 1D, 2D, and 3D

Suggested optimization strategies based on auxiliary field visualization

Abstract

The push-relabel algorithm can be used to calculate rapidly the exact ground states for a given sample with a random-field Ising model (RFIM) Hamiltonian. Although the algorithm is guaranteed to terminate after a time polynomial in the number of spins, implementation details are important for practical performance. Empirical results for the timing in dimensions d=1,2, and 3 are used to determine the fastest among several implementations. Direct visualization of the auxiliary fields used by the algorithm provides insight into its operation and suggests how to optimize the algorithm. Recommendations are given for further study of the RFIM.