Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries
Statistical Mechanics
2008-11-26 v1 High Energy Physics - Lattice
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.cond-mat/0306362,
title = {Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries},
author = {A. C. D. van Enter and S. B. Shlosman},
journal= {arXiv preprint arXiv:cond-mat/0306362},
year = {2008}
}