  The problem of the phase transition of a Z(3) spin system is a complex issue.
A numerical simulation in the framework of the mean field theory using the
Metropolis algorithm reveals: (a) the existence of second order phase
transition with a degenerated critical point which could be considered as a
state of resonance (b) hysteresis phenomena which are accompanied with
tricritical crossover around the end point of first order transition. Based on
these results we propose a scenario about confinement-deconfinement phase
transition in SU(3) symmetry of color QCD which, as it is known, has the same
center with Z(3) spin system symmetry.
