Random clusters in the Villain and XY models
Probability
2022-11-30 v2 Mathematical Physics
math.MP
Abstract
In the Ising and Potts model, random cluster representations provide a geometric interpretation to spin correlations. We discuss similar constructions for the Villain and XY models, where spins take values in the circle, as well as extensions to models with different single site spin spaces. In the Villain case, we highlight natural interpretation in terms of the cable system extension of the model. We also list questions and open problems on the cluster representations obtained in this fashion.
Cite
@article{arxiv.2210.03620,
title = {Random clusters in the Villain and XY models},
author = {Julien Dubédat and Hugo Falconet},
journal= {arXiv preprint arXiv:2210.03620},
year = {2022}
}
Comments
v2: minor edits and references added. 30 pages, 4 figures