One dimensional spin glasses with potential decay \(1/r^{1+\epsilon}\). Absence of phase transitions and cluster properties
type: Item
instance of: scholarly article
title: One dimensional spin glasses with potential decay \(1/r^{1+\epsilon}\). Absence of phase transitions and cluster properties
zbMATH Open document ID: 0615.60099
DOI: 10.1007/BF01210614
author: A. C. D. van Enter
author: Massimo Campanino
author: E. Olivieri
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: In this paper the one-dimensional Ising spin model with two-body random potential is considered decaying with the distance like \(1/r^{1+\epsilon}\). Assuming that the boundary conditions are independent of the random realisation of the interaction it is proved that with large probability the Gibbs expectation of an observable localized far away from the boundary of finite volume has a weak dependence on the boundary conditions. It is established also that the limiting Gibbs state exists which is a pure state and satisfies some mixing property. Moreover, with probability one, any two boundary conditions generate the same Gibbs state.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3996826
zbMATH Keywords: spin glasses
zbMATH Keywords: nearest neighbour block model
zbMATH Keywords: Ising spin model
zbMATH Keywords: weak dependence
zbMATH Keywords: Gibbs state
zbMATH Keywords: mixing property
zbMATH Keywords: boundary conditions
reviewed by: S. Poghosyan
MaRDI profile type: Publication
cites work: Analyticity for one-dimensional systems with long-range superstable interactions
cites work: Infinite differentiability for one-dimensional spin system with long range random interaction
cites work: Absence of symmetry breaking for \(N\)-vector spin glass models in two dimensions
cites work: Absence of phase transitions in certain one-dimensional long-range random systems
full work available at URL: https://doi.org/10.1007/bf01210614
OpenAlex ID: W2149750449
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description: scientific article; zbMATH DE number 3996826