On the comparison of optimization algorithms for the random-field Potts model

TL;DR

This paper compares various approximate algorithms for finding ground states in the NP-hard random-field Potts model, highlighting their efficiency and accuracy in systems with discrete degrees of freedom.

Contribution

It provides a systematic evaluation of approximate methods for the complex random-field Potts model, which is computationally challenging due to its NP-hardness.

Findings

Some algorithms achieve near-optimal solutions efficiently.

Performance varies significantly across different system sizes.

Approximate techniques can be effective for large systems despite NP-hardness.

Abstract

For many systems with quenched disorder the study of ground states can crucially contribute to a thorough understanding of the physics at play, be it for the critical behavior if that is governed by a zero-temperature fixed point or for uncovering properties of the ordered phase. While ground states can in principle be computed using general-purpose optimization algorithms such as simulated annealing or genetic algorithms, it is often much more efficient to use exact or approximate techniques specifically tailored to the problem at hand. For certain systems with discrete degrees of freedom such as the random-field Ising model, there are polynomial-time methods to compute exact ground states. But even as the number of states increases beyond two as in the random-field Potts model, the problem becomes NP hard and one cannot hope to find exact ground states for relevant system sizes. Here, we compare a number of approximate techniques for this problem and evaluate their performance.