On the mean-field spin glass transition
| Autor: | L. DeSanctis, Adriano Barra |
|---|---|
| Přispěvatelé: | Barra, Adriano, Desanctis, L. |
| Jazyk: | angličtina |
| Rok vydání: | 2008 |
| Předmět: |
Physics
Spin glass Cavity method Complex system Statistical mechanics Condensed Matter Physics Condensed Matter::Disordered Systems and Neural Networks Critical point (mathematics) Electronic Optical and Magnetic Materials Mean field theory Quantum mechanics Complete theory Statistical physics Symmetry breaking |
| Popis: | In this paper we analyze two main prototypes of disordered mean-field systems, namely the Sherrington-Kirkpatrick (SK) and the Viana-Bray (VB) models, to show that, in the framework of the cavity method, the transition from the annealed regime to a broken replica symmetry phase can be thought of as the failure of the saturability property (detailed explained along the paper) of the overlap fluctuations which act as the order parameters of the theory. We show furthermore how this coincides with the lacking of the commutativity of the infinite volume limit with respect to a, suitably chosen, vanishing perturbing field inducing the transition as prescribed by standard statistical mechanics. This is another step towards a complete theory of disordered systems. As a well known consequence it turns out that the annealed and the replica symmetric regions must coincide, implying that the averaged overlap is zero in this phase. Within our framework the finding of the values of the critical point for the SK and line for the VB becomes available straightforwardly and the method is of a large generality and applicable to several other mean field models |
| Databáze: | OpenAIRE |
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