Quasi-exact ground-state algorithm for the random-field Potts model

TL;DR

This paper introduces a quasi-exact algorithm combining graph cut methods and repeated runs to approximate ground states of the NP-hard random-field Potts model, enabling systematic extrapolation of system properties.

Contribution

It presents a novel approach that leverages multiple runs of approximation algorithms to estimate ground states in the challenging random-field Potts model.

Findings

Method accurately approximates ground states for benchmark samples.

Systematic extrapolation improves understanding of disordered systems.

Approach extends computational capabilities beyond existing exact algorithms.

Abstract

The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While for this system exact ground states can be computed efficiently in polynomial time, the related random-field Potts model is {\em NP\} hard computationally. While thus exact ground states cannot be computed for large systems in this case, approximation schemes based on graph cuts and related techniques can be used. Here we show how a combination of such methods with repeated runs allows for a systematic extrapolation of relevant system properties to the ground state. The method is benchmarked on a special class of disorder samples for which exact ground states are available.