Equilibrium properties of disordered spin models with two-scale interactions

Abstract

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

Publication DOI: https://doi.org/10.1103/PhysRevE.80.031138
Divisions: Engineering & Applied Sciences
Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: © 2009 The American Physical Society.
Uncontrolled Keywords: classical disordered spin systems,equilibrium properties,Sherrington-Kirkpatrick model,sparse Erdös-Rényi graph structures,percolation threshold,Bethe lattices,sparse strong interactions,weak dense interactions,Condensed Matter Physics,Statistical and Nonlinear Physics,Statistics and Probability
Full Text Link: http://pre.aps. ... /v80/i3/e031138
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2009-09-24
Authors: Raymond, Jack
Saad, David ( 0000-0001-9821-2623)

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