  Infinite-range spin-glass models with Levy-distributed interactions show a
freezing transition similar to disordered spin systems on finite connectivity
random graphs. It is shown that despite diverging moments of the local field
distribution this transition can be analyzed within the replica approach by
working at imaginary temperature and using a variant of the replica method
developed for diluted systems and optimization problems. The replica-symmetric
self-consistent equation for the distribution of local fields illustrates how
the long tail in the distribution of coupling strengths gives rise to a
significant fraction of strong bonds per spin which form a percolating backbone
at the transition temperature.
