A mathematical reformulation of Derrida's REM and GREM
type: Item
instance of: scholarly article
title: A mathematical reformulation of Derrida's REM and GREM
zbMATH Open document ID: 0617.60100
DOI: 10.1007/BF01210613
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The author investigates two statistical models introduced by \textit{B. Derrida} and called respectively random energy model (REM) [Random-energy model: Limit of a family of disordered models, Phys. Rev. Lett. 45, 79-82 (1982), and Random-energy model: An exactly solvable model of disordered systems, Phys. Rev. B 24, 2613-2626 (1981)] and general random energy model (GREM) [A generalization of the random energy model which includes correlations between energies, J. Phys. Lett. 46, L401-L407 (1985), and \textit{B. Derrida} and \textit{E. Gardner}, Solution of the generalized random energy model, J. Phys. C, in press (1986)]. In Derrida's original formulation of the REM and GREM certain limits are implicit. By means of a modification of the Poisson distribution on the corresponding configurational space the author gives a mathematical reformulation where these limits have already been taken. It permits for instance to perform more systematic calculations of relevance to Parisi's solution of the Sherrington-Kirkpatrick spin-glass model.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4001167
zbMATH Keywords: probability cascades
zbMATH Keywords: random energy model
zbMATH Keywords: Poisson distribution
zbMATH Keywords: spin- glass model
author: David Ruelle
reviewed by: S. Poghosyan
MaRDI profile type: Publication
cites work: Random-energy model: An exactly solvable model of disordered systems
cites work: Replica symmetry breaking and the nature of the spin glass phase
full work available at URL: https://doi.org/10.1007/bf01210613
OpenAlex ID: W2092526846
description: scientific article; zbMATH DE number 4001167