English

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}
}
R2 v1 2026-06-23T23:58:11.729Z