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Haakeâ€"Lewensteinâ€"Wilkens approach to spin-glasses revisited.

Authors :
Lewenstein, Maciej
Cirauqui, David
Ángel GarcĂ-a-March, Miguel
GuigĂł i Corominas, Guillem
Grzybowski, Przemysław
Saavedra, José R M
Wilkens, Martin
Wehr, Jan
Source :
Journal of Physics A: Mathematical & Theoretical; 11/11/2022, Vol. 55 Issue 45, p1-20, 20p
Publication Year :
2022

Abstract

We revisit the Haakeâ€"Lewensteinâ€"Wilkens approach to Edwardsâ€"Anderson (EA) model of Ising spin glass (SG) (Haake et al 1985 Phys. Rev. Lett. 55 2606). This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, q EA . We use saddle point/steepest descent (SPSD) method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that q EA > 0 at 0 < T < T c in 3D and 4D. The case of 2D seems to be a little more subtle, since in the present approach energy increase for a domain wall competes with boundary/edge effects more strongly in 2D; still our approach predicts SG order at sufficiently low temperature. We speculate, how these predictions confirm/contradict widely spread opinions that: (i) There exist only one (up to the spin flip) ground state in EA model in 2D, 3D and 4D; (ii) there is (no) SG transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
17518113
Volume :
55
Issue :
45
Database :
Complementary Index
Journal :
Journal of Physics A: Mathematical & Theoretical
Publication Type :
Academic Journal
Accession number :
160134550
Full Text :
https://doi.org/10.1088/1751-8121/ac9d10