Communications in Mathematical Physics

, Volume 226, Issue 2, pp 433–454 | Cite as

2D Models of Statistical Physics with Continuous Symmetry: The Case of Singular Interactions

  • D. Ioffe
  • S. Shlosman
  • Y. Velenik


We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular interactions with continuous symmetry, when the symmetry is broken in the thermodynamic limit.


Statistical Physic Symmetry Breaking Thermodynamic Limit Lattice System Continuous Symmetry 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • D. Ioffe
    • 1
  • S. Shlosman
    • 2
  • Y. Velenik
    • 3
  1. 1.Dept. of Industrial Engineering, Technion, Haifa, Israel. E-mail:
  2. 2.CPT, Luminy, Marseille, France. E-mail: shlosman@cpt.univ-mrs.frFR
  3. 3.UMR-CNRS 6632, CMI, Marseille, France. E-mail: velenik@cmi.univ-mrs.frFR

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