The Hierarchical Random Energy Model
Statistical Mechanics
2014-09-09 v3 Disordered Systems and Neural Networks
Abstract
We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin glass condensation transition similar to the one occuring in the usual mean field Random Energy Model. At variance with mean field, the high temperature branch of the free-energy is non-analytic at the transition point.
Keywords
Cite
@article{arxiv.0912.3634,
title = {The Hierarchical Random Energy Model},
author = {Michele Castellana and Aurelien Decelle and Silvio Franz and Marc Mezard and Giorgio Parisi},
journal= {arXiv preprint arXiv:0912.3634},
year = {2014}
}