  The phase diagram of the two- and three-state Potts model with infinite-range
interactions, in the external field is analyzed by studying the partition
function zeros in the complex field plane. The tricritical point of the
three-state model is observed as the approach of the zeros to the real axis at
the nonzero field value. Different regimes, involving several first- and
second-order transitions of the complicated phase diagram of the three state
model are identified from the scaling properties of the zeros closest to the
real axis. The critical exponents related to the tricritical point and the
Yang-Lee edge singularity are well reproduced. Calculations are extended to the
negative fields, where the exact implicit expression for the transition line is
derived.
