The Lévy spin glass transition

We determine the phase transition in the Lévy 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 $\rightarrow$ 0 limit and determine the de Almeida-Thouless transition temperature in the 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.