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Counting metastable states of Ising spin glasses on arbitrary graphs

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Original languageEnglish
Article number041114
Pages (from-to)-
Number of pages7
JournalPhysical Review E - Statistical, Nonlinear and Soft Matter Physics
Issue number4
Publication statusPublished - Apr 2008


Using a field-theoretical representation of the Tanaka-Edwards integral, we develop a method to systematically compute the number N-s of one-spin stable states (local energy minima) of a glassy Ising system with nearest-neighbor interactions and random Gaussian couplings on an arbitrary graph. In particular, we use this method to determine N-s for K-regular random graphs and d-dimensional regular lattices for d=2,3. The method works also for other graphs. Excellent accuracy of the results allows us to observe that the number of local energy minima depends mainly on local properties of the graph on which the spin glass is defined.

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