Equilibrium properties of disordered spin models with two-scale interactions

Raymond, Jack and Saad, David (2009). Equilibrium properties of disordered spin models with two-scale interactions. Physical review E, 80 (3), 031138.

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Official URL: http://pre.aps.org/abstract/PRE/v80/i3/e031138

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.

Item Type:Article
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
Divisions:Schools_of_Study > Engineering & Applied Science
Schools_of_Study > Engineering & Applied Science > Mathematics (EAS)
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ID Code:9292
Deposited By:David Saad
Deposited On:29 Jul 2010 11:14
Last Modified:12 Mar 2014 08:07

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