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.

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
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
Published Date: 2009-09-24

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