Classical XY Model in 1.99 Dimensions
Statistical Mechanics
2009-10-30 v1
Abstract
We consider the classical XY model (O(2) nonlinear sigma-model) on a class of lattices with the (fractal) dimensions 1<D<2. The Berezinskii's harmonic approximation suggests that the model undergoes a phase transition in which the low temperature phase is characterized by stretched exponential decay of correlations. We prove an exponentially decaying upper bound for the two-point correlation functions at non-zero temperatures, thus excluding the possibility of such a phase transition.
Keywords
Cite
@article{arxiv.cond-mat/9708126,
title = {Classical XY Model in 1.99 Dimensions},
author = {Tohru Koma and Hal Tasaki},
journal= {arXiv preprint arXiv:cond-mat/9708126},
year = {2009}
}
Comments
LaTeX 8 pages, no figures