Communications in Mathematical Physics

, Volume 274, Issue 1, pp 81–122 | Cite as

Translation-Invariance of Two-Dimensional Gibbsian Point Processes

  • Thomas RichthammerEmail author


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.


Point Process Hard Core Gibbs Measure Lexicographic Order Translational Symmetry 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität MünchenMünchenGermany

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