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Two-dimensional Gibbsian point processes with continuous spin symmetries

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  • Richthammer, Thomas

Abstract

The conservation of continuous symmetries in two-dimensional systems with interaction is a classical subject of statistical mechanics. So far, all results of this sort required some smoothness properties of the interaction. Only recently Ioffe et al. (Comm. Math. Phys. 226 (2002) 433) succeeded to treat the case of lattice systems with continuous, rather than smooth, interaction. Here we establish a similar result for Gibbsian systems of point particles with internal degrees of freedom.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:5:p:827-848
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    Cited by:

    1. 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.
    2. 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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