Random currents expansion of the Ising model
Abstract
Critical behavior at an order/disorder phase transition has been a central object of interest in statistical physics. In the past century, techniques borrowed from many different fields of mathematics (Algebra, Combinatorics, Probability, Complex Analysis, Spectral Theory, etc) have contributed to a more and more elaborate description of the possible critical behaviors for a large variety of models. The Ising model is maybe one of the most striking success of this cross-fertilization, for this model of ferromagnetism is now very well understood both physically and mathematically. In this article, we review an approach, initiated in \cite{GriHurShe70,Aiz82} and based on the notion of random currents, enabling a deep study of the model.
Cite
@article{arxiv.1607.06933,
title = {Random currents expansion of the Ising model},
author = {Hugo Duminil-Copin},
journal= {arXiv preprint arXiv:1607.06933},
year = {2017}
}
Comments
Proceedings of the 7th European Congress of Mathematicians in Berlin