Genetic embedded matching approach to ground states in continuous-spin systems

TL;DR

This paper introduces a novel genetic algorithm-based heuristic for efficiently finding ground states in continuous-spin systems, addressing the challenge posed by their complex energy landscapes.

Contribution

It presents a new optimization method combining Ising spin embedding with genetic algorithms tailored for continuous spins, improving ground state search.

Findings

The method reliably finds ground states in continuous-spin systems.

Benchmarking shows superior performance over simulated annealing.

Statistical techniques ensure high reliability in results.

Abstract

Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be NP-hard in the most general case. Owing to the specific structure of local (free) energy minima, general-purpose optimization strategies perform relatively poorly on these problems, and a number of specially tailored optimization techniques have been developed in particular for the Ising spin glass and similar discrete systems. Here, an efficient optimization heuristic for the much less discussed case of continuous spins is introduced, based on the combination of an embedding of Ising spins into the continuous rotators and an appropriate variant of a genetic algorithm. Statistical techniques for insuring high reliability in finding (numerically) exact ground states are discussed, and the method is benchmarked against the simulated annealing approach.