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Phase transitions of hard sphere lattice gases

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Abstract

A unified proof is given for the existence of a phase transition for any two or three dimensional lattice gas with hard cores excluding nearest neighbor occupancy, provided only that the lattice is an open one (possessing two sublattices). It is not required that one sublattice be a translate of the other. Consequently the proof applies to the plane hexagonal and to the diamond lattices, as well as the “cubic” lattices previously proved to have phase transitions. The models are converted to equivalent Ising spin 1/2 systems on one sublattice by a “partial trace” over the other. The spin system has many-spin interactions including some of odd order, which destroys up-down symmetry, but recent work of Pirogov and Sinai on such systems is shown to be applicable and to prove the existence of the phase transition.

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Authors and Affiliations

  1. Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana, USA

    L. K. Runnels

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  1. L. K. Runnels
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Communicated by G. Gallavotti

Supported in part by National Science Foundation Grant No. GP 33535X.

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Runnels, L.K. Phase transitions of hard sphere lattice gases. Commun.Math. Phys. 40, 37–48 (1975). https://doi.org/10.1007/BF01614095

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  • DOI: https://doi.org/10.1007/BF01614095

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