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

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  • Richthammer, Thomas

Abstract

One of the main objectives of equilibrium state statistical physics is to analyze which symmetries of an interacting particle system in equilibrium are 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.

Suggested Citation

  • Richthammer, Thomas, 2009. "Translation invariance of two-dimensional Gibbsian systems of particles with internal degrees of freedom," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 700-736, March.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:3:p:700-736
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    References listed on IDEAS

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    1. Richthammer, Thomas, 2005. "Two-dimensional Gibbsian point processes with continuous spin symmetries," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 827-848, May.
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    Cited by:

    1. Yuri Suhov & Mark Kelbert & Izabella Stuhl, 2020. "The Feynman–Kac Representation and Dobrushin–Lanford–Ruelle States of a Quantum Bose-Gas," Mathematics, MDPI, vol. 8(10), pages 1-41, October.
    2. Fiedler, Michael & Richthammer, Thomas, 2021. "A lower bound on the displacement of particles in 2D Gibbsian particle systems," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 1-32.

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    1. Yuri Suhov & Mark Kelbert & Izabella Stuhl, 2020. "The Feynman–Kac Representation and Dobrushin–Lanford–Ruelle States of a Quantum Bose-Gas," Mathematics, MDPI, vol. 8(10), pages 1-41, October.

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