An elementary proof of phase transition in the planar XY model
Mathematical Physics
2022-11-30 v2 math.MP
Probability
Abstract
Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first rigorously obtained by Fr\"{o}hlich and Spencer and establishes a Berezinskii-Kosterlitz-Thouless phase transition in the model. Our argument relies on a new loop representation of spin correlations, a recent result of Lammers on delocalisation of integer-valued height functions, and classical correlation inequalities.
Keywords
Cite
@article{arxiv.2110.09465,
title = {An elementary proof of phase transition in the planar XY model},
author = {Diederik van Engelenburg and Marcin Lis},
journal= {arXiv preprint arXiv:2110.09465},
year = {2022}
}
Comments
25 pages, statement of main result slightly improved