Communications in Mathematical Physics

, Volume 255, Issue 1, pp 21–32 | Cite as

Provable First-Order Transitions for Nonlinear Vector and Gauge Models with Continuous Symmetries

  • Aernout C. D. van EnterEmail author
  • Senya B. Shlosman


We consider various sufficiently nonlinear vector models of ferromagnets, of nematic liquid crystals and of nonlinear lattice gauge theories with continuous symmetries. We show, employing the method of Reflection Positivity and Chessboard Estimates, that they all exhibit first-order transitions in the temperature, when the nonlinearity parameter is large enough. The results hold in dimension 2 or more for the ferromagnetic models and the RP N −1 liquid crystal models and in dimension 3 or more for the lattice gauge models. In the two-dimensional case our results clarify and solve a recent controversy about the possibility of such transitions. For lattice gauge models our methods provide the first proof of a first-order transition in a model with a continuous gauge symmetry.


Gauge Theory Liquid Crystal Gauge Symmetry Nematic Liquid Crystal Vector Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Centre for Theoretical PhysicsRijksuniversiteit GroningenGroningenThe Netherlands
  2. 2.CPT, CNRS Luminy, Case 907Marseille Cedex 9France
  3. 3.IITP, RASMoscowRussia

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