On the mean-field equations for ferromagnetic spin systems
Mathematical Physics
2021-08-10 v4 math.MP
Probability
Abstract
We derive mean-field equations for a general class of ferromagnetic spin systems with an explicit error bound in finite volumes. The proof is based on a link between the mean-field equation and the free convolution formalism of random matrix theory, which we exploit in terms of a dynamical method. We present three sample applications of our results to Ka\'{c} interactions, randomly diluted models, and models with an asymptotically vanishing external field.
Keywords
Cite
@article{arxiv.2103.06207,
title = {On the mean-field equations for ferromagnetic spin systems},
author = {Christian Brennecke and Per von Soosten},
journal= {arXiv preprint arXiv:2103.06207},
year = {2021}
}