Highly anisotropic scaling limits
Abstract
We consider a highly anisotropic Ising spin model whose precise definition can be found at the beginning of Section 2. In this model the spins on a same horizontal line (layer) interact via a Kac potential while the vertical interaction is between nearest neighbors, both interactions being ferromagnetic. The temperature is set equal to 1 which is the mean field critical value, so that the mean field limit for the Kac potential alone does not have a spontaneous magnetization. We compute the phase diagram of the full system in the Lebowitz-Penrose limit showing that due to the vertical interaction it has a spontaneous magnetization. The result is not covered by the Lebowitz-Penrose theory because our Kac potential has support on regions of positive codimension.
Cite
@article{arxiv.1507.05770,
title = {Highly anisotropic scaling limits},
author = {Marzio Cassandro and Matteo Colangeli and Errico Presutti},
journal= {arXiv preprint arXiv:1507.05770},
year = {2016}
}