English

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}
}