  We study the sign distribution of generalized magnetic susceptibilities in
the temperature-external magnetic field plane using the three-dimensional
three-state Potts model. We find that the sign of odd-order susceptibility is
opposite in the symmetric (disorder) and broken (order) phases, but that of the
even-order one remains positive when it is far away from the phase boundary.
When the critical point is approached from the crossover side, negative
fourth-order magnetic susceptibility is observable. It is also demonstrated
that non-monotonic behavior occurs in the temperature dependence of the
generalized susceptibilities of the energy. The finite-size scaling behavior of
the specific heat in this model is mainly controlled by the critical exponent
of the magnetic susceptibility in the three-dimensional Ising universality
class.
