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Two-dimensional Gibbsian point processes with continuous spin-symmetries

Thomas Richthammer
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Abstract

We consider two-dimensional marked point processes which are Gibbsian with a two-body-potential U. U is supposed to have an internal continuous symmetry. We show that under suitable continuity conditions the considered processes are invariant under the given symmetry. We will achieve this by using Ruelle`s superstability estimates and percolation arguments.

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Thomas Richthammer. 2004-07-13. Two-dimensional Gibbsian point processes with continuous spin-symmetries. https://arxiv.org/abs/math/0407216

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