Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries
A. C. D. van Enter, S. B. Shlosman
Abstract
We consider various sufficiently nonlinear sigma models for nematic liquid crystal ordering of RPN-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 RPN-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 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.
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