  We show that systems with negative specific heat can violate the zeroth law
of thermodynamics. By both numerical simulations and by using exact expressions
for free energy and microcanonical entropy it is shown that if two systems with
the same intensive parameters but with negative specific heat are thermally
coupled, they undergo a process in which the total entropy increases
irreversibly. The final equilibrium is such that two phases appear, that is,
the subsystems have different magnetizations and internal energies at
temperatures which are equal in both systems, but that can be different from
the initial temperature.
