03-278 van Enter A.C.D., Shlosman S.B.

Provable forst-order transitions for liquid crystal and lattice gauge models with continuous symmetries (29K, LATeX) Jun 13, 03

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Abstract. We consider various sufficiently nonlinear sigma models for nematic ordering of RP^{N-1} type and of lattice gauge type with continous symmetries. We rigorously show that they exhibit a first-order transition in the temperature. The result holds in dimension 2 or more for the RP{N-1} 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 possibilty of such transitions. For lattice gauge models our methods provide the first prof of a first-order transition in a model with a continous gauge symmetry.

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