The Levy spin glass transition

We determine the phase transition of the Levy spin glass. A regularized model where the coupling constants smaller than some cutoff $ε$ are neglected can be studied by the cavity method for diluted spin glasses. We show how to handle the $ε\to 0$ limit and determine the de Almeida-Thouless transition temperature in presence of an external field. Contrary to previous findings, in zero external field we do not find any stable replica-symmetric spin glass phase: the spin glass phase is always a replica-symmetry-broken phase.

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