A spin-glass model with random couplings
type: Item
instance of: scholarly article
title: A spin-glass model with random couplings
zbMATH Open document ID: 0553.60098
DOI: 10.1007/BF01258536
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: A spin-glass model is studied, which is similar to the one treated by the authors, \textit{V. Glaser} and \textit{A. Martin}, A spin glass with random couplings. J. Stat. Phys. 36, 89-106 (1984). The lattice and the type of the interaction are the same, the models differ in the assumption on the distribution of the interaction. In the present paper the random couplings are independent identically distributed, whereas in the other one certain couplings coincide. This causes frustration in the present case. The main topic of the paper is the behaviour of the effective random couplings under a change of scale, which leads to a renormalization group approach. The low and high temperature behaviour are studied. The existence of a critical fixed point and of a transition of the Edward-Anderson parameter is shown. The authors emphasize that their results can be viewed as an example of non-trivial behaviour of non-independent, but not strongly coupled random variables.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 3881647
zbMATH Keywords: Edward-Anderson transition
zbMATH Keywords: spin-glass model
zbMATH Keywords: random couplings
zbMATH Keywords: renormalization group
zbMATH Keywords: critical fixed point
author: P. Collet
author: Jean-Pierre Eckmann
MaRDI profile type: Publication
cites work: Universal properties of maps on an interval
cites work: Q4085018
cites work: Limit Theorems for Densities and Asymptotic Expansions for Distributions of Sums of Independent Random Variables
full work available at URL: https://doi.org/10.1007/bf01258536
OpenAlex ID: W2036479224
description: scientific article; zbMATH DE number 3881647