The cluster expansion method provides a standard framework to map first-principles generated energies for a few selected configurations of a binary alloy onto a finite set of pair and many-body interactions between the alloyed elements. These interactions describe the energetics of all possible configurations of the same alloy, which can hence be readily used to identify ground state structures and, through statistical mechanics solutions, find finite-temperature properties. In practice, the biggest challenge is to identify the types of interactions which are most important for a given alloy out of the many possibilities. We describe a genetic algorithm which automates this task. To avoid a possible trapping in a locally optimal interaction set, we periodically "lock out" persistent near-optimal cluster expansions. In this way, we identify not only the best possible combination of interaction types but also any near-optimal cluster expansions. Our strategy is not restricted to the cluster expansion method alone, and can be applied to select the qualitative parameter types of any other class of complex model Hamiltonians.

Original Publication Citation

Volker Blum, Gus L. W. Hart, Michael Walorski*, and Alex Zunger, "Using genetic algorithms to develop model Hamiltonians: Applications to the generalized Ising model," Phys. Rev. B 72 165113 (26 Oct. 25). The original article may be found here: http://prb.aps.org/abstract/PRB/v72/i16/e165113

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Peer-Reviewed Article

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The American Physical Society




Physical and Mathematical Sciences


Physics and Astronomy