  Infinite-range spin-glass models with Levy-distributed interactions show a
spin-glass transition with similarities to both the Sherrington-Kirkpatrick
model and to disordered spin systems on finite connectivity random graphs.
Despite the diverging moments of the coupling distribution the transition can
be analyzed within the replica approach by working at imaginary temperature.
Within the replica-symmetric approximation a self-consistent equation for the
distribution of local fields is derived and from the instability of the
paramagnetic solution to this equation the glass-transition temperature is
determined. The role of the percolation of rare strong bonds for the transition
is elucidated. The results partly agree and partly disagree with those obtained
within the cavity approach. Numerical simulations using parallel tempering are
in agreement with the transition temperatures found.
