A Multi-Scale Spin-Glass Mean-Field Model
Mathematical Physics
2019-02-20 v3 math.MP
Abstract
In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied. The pressure per particle in the thermodynamical limit is proved to obey a variational principle of Parisi type. The result is achieved by means of lower and upper bounds. The lower bound is obtained with a Ruelle cascade using the interpolation technique, while the upper bound exploits factorisation properties of the equilibrium measure and the synchronisation technique
Cite
@article{arxiv.1804.00629,
title = {A Multi-Scale Spin-Glass Mean-Field Model},
author = {Pierluigi Contucci and Emanuele Mingione},
journal= {arXiv preprint arXiv:1804.00629},
year = {2019}
}
Comments
Minor changes, references added. To appear in Communication in Mathematical Physics