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Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries

A. C. D. van Enter·S. B. Shlosman
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Abstract

We consider various sufficiently nonlinear sigma models for nematic liquid crystal 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 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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A. C. D. van Enter, S. B. Shlosman. 2003-06-13. Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries. https://doi.org/10.1007/s00220-004-1286-1

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