On the REM approximation of TAP free energies
Disordered Systems and Neural Networks
2023-07-19 v1 Probability
Abstract
The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical large deviations treatment. This allows to identify the origin of the physically unsettling quadratic (in the inverse of temperature) correction to the Parisi free energy for the SK-model, and formalizes the cavity dynamics which acts on TAP-space, i.e. on the space of TAP-solutions. From a non-spin glass point of view, this work is the first in a series of refinements which addresses the stability of hierarchical structures in models of evolving populations.
Keywords
Cite
@article{arxiv.2212.11718,
title = {On the REM approximation of TAP free energies},
author = {Nicola Kistler and Marius Alexander Schmidt and Giulia Sebastiani},
journal= {arXiv preprint arXiv:2212.11718},
year = {2023}
}