On the REM approximation of TAP free energies

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 true 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.

Metadaten
Author:	Nicola Kistler ORCiD GND, Marius Alexander Schmidt GND, Giulia Sebastiani GND
URN:	urn:nbn:de:hebis:30:3-857385
URL:	https://arxiv.org/abs/2212.11718v1
DOI:	https://doi.org/10.48550/arXiv.2212.11718
Parent Title (English):	arXiv
Publisher:	arXiv
Document Type:	Preprint
Language:	English
Date of Publication (online):	2022/12/22
Date of first Publication:	2022/12/22
Publishing Institution:	Universitätsbibliothek Johann Christian Senckenberg
Release Date:	2024/06/13
Issue:	2212.11718 Version 1
Edition:	Version 1
Page Number:	28
Institutes:	Informatik und Mathematik / Mathematik
Dewey Decimal Classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G70 Extreme value theory; extremal processes
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
	82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Bxx Equilibrium statistical mechanics / 82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)
Sammlungen:	Universitätspublikationen
Licence (German):	Creative Commons - CC BY - Namensnennung 4.0 International

Open Access