Haake-Lewenstein-Wilkens approach to spin-glasses revisited

Maciej Lewenstein, David Cirauqui, Miguel Ángel García-March, Guillem Guigó i Corominas, Przemysław Grzybowski, José R.M. Saavedra, Martin Wilkens, Jan Wehr

Research output: Contribution to journalArticlepeer-review


We revisit the Haake-Lewenstein-Wilkens approach to Edwards-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.

Original languageEnglish (US)
Article number454002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number45
StatePublished - Nov 11 2022


  • Edwards-Anderson order parameter
  • Haake-Lewenstein-Wilkens approach
  • Saddle Point/Steppest Descend method
  • spin glass

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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