  We determine the phase transition of the Levy spin glass. A regularized model
where the coupling constants smaller than some cutoff $\epsilon$ are neglected
can be studied by the cavity method for diluted spin glasses. We show how to
handle the $\epsilon\to 0$ 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.
