  We study the partition-function zeros in mean-field spin-glass models. We
show that the replica method is useful to find the locations of zeros in a
complex parameter plane. For the random energy model, we obtain the phase
diagram in the plane and find that there are two types of distribution of
zeros: two-dimensional distribution within a phase and one-dimensional one on a
phase boundary. Phases with a two-dimensional distribution are characterized by
a novel order parameter defined in the present replica analysis. We also
discuss possible patterns of distributions by studying several systems.
