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Predicting long- and short-range order with restricted Boltzmann machine

Generalization properties of the restricted Boltzmann machine (RBM) for two-dimensional Ising model are investigated. Both long-range and short-range order are examined: the first is studied for a spin lattice with ferromagnetic interaction, and the second is considered for a binary alloy on the square lattice. For each of these cases, algorithms are proposed that allow the once trained RBM to predict the order parameters for any temperature and alloy concentration.