Abstract
The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general.
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Communicated by H. Spohn
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Richthammer, T. Translation-Invariance of Two-Dimensional Gibbsian Point Processes. Commun. Math. Phys. 274, 81–122 (2007). https://doi.org/10.1007/s00220-007-0274-7
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DOI: https://doi.org/10.1007/s00220-007-0274-7