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Due to an extremely rugged structure of the free energy landscape, thedetermination of spin-glass ground states is among the hardest knownoptimization problems, found to be NP-hard in the most general case. Owing tothe specific structure of local (free) energy minima, general-purposeoptimization strategies perform relatively poorly on these problems, and anumber of specially tailored optimization techniques have been developed inparticular for the Ising spin glass and similar discrete systems. Here, anefficient optimization heuristic for the much less discussed case of continuousspins is introduced, based on the combination of an embedding of Ising spinsinto 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 thesimulated annealing approach.

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