Translation invariance of two-dimensional Gibbsian systems of particles with internal degrees of freedom

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Richthammer, Thomas

关键词: Gibbs measures;    Mermin-Wagner theorem;    Translation;    Hard core;    Singularity;    Widom-Rowlinson model;    Potts model;    Percolation;   

DOI  :  10.1016/j.spa.2008.04.001

来源: Elsevier

【 摘 要 】

One of the main objectives of equilibrium state statistical physics is to analyze which symmetries of an interacting particle system in equilibrium arc broken or conserved. Here we present a general result on the conservation of translational symmetry for two-dimensional Gibbsian particle systems. The result applies to particles with internal degrees of freedom and fairly arbitrary interaction, including the interesting cases of discontinuous, singular, and hard core interaction. In particular we thus show the conservation of' translational symmetry for the continuum Widom-Rowlinson model and a class of continuum Potts type models. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free