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The global minimum of energy is not always a sum of local minima—A note on frustration

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Abstract

A classical lattice gas model with translation-invariant, finite-range competing interactions, for which there does not exist an equivalent translation-invariant, finite-range nonfrustrated potential, is constructed. The construction uses the structure of nonperiodic ground-state configurations of the model. In fact, the model does not have any periodic ground-state configurations. However, its ground-state—a translation-invariant probability measure supported by ground-state configurations—is unique.

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Authors and Affiliations

  1. Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, 3001, Heverlee, Belgium

    Jacek Mieisz

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  1. Jacek Mieisz
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Mieisz, J. The global minimum of energy is not always a sum of local minima—A note on frustration. J Stat Phys 71, 425–434 (1993). https://doi.org/10.1007/BF01058430

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  • DOI: https://doi.org/10.1007/BF01058430

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