Rigorous Results for Hierarchical Models of Structural Glasses
Mathematical Physics
2014-09-09 v3 Disordered Systems and Neural Networks
math.MP
Abstract
We consider two non-mean-field models of structural glasses built on a hierarchical lattice. First, we consider a hierarchical version of the random energy model (HREM), and we prove the existence of the thermodynamic limit and self-averaging of the free energy. Furthermore, we prove that the infinite-volume entropy is positive in a high-temperature region bounded from below, thus providing an upper bound on the Kauzmann critical temperature. In addition, we show how to improve this bound by leveraging the hierarchical structure of the model. Finally, we introduce a hierarchical version of the -spin model of a structural glass, and we prove the existence of the thermodynamic limit and self-averaging of the free energy.
Keywords
Cite
@article{arxiv.1403.5667,
title = {Rigorous Results for Hierarchical Models of Structural Glasses},
author = {Michele Castellana},
journal= {arXiv preprint arXiv:1403.5667},
year = {2014}
}