  The spherical spin model with infinite-range ferromagnetic interactions is
investigated analytically in the framework of non-extensive thermostatics
generalizing the Boltzmann-Gibbs statistical mechanics. We show that for
repulsive correlations, a new weak-ferromagnetic phase develops. There is a
tricritical point separating para, weak-ferro and ferro regimes. The transition
from paramagnetic to weak-ferromagnetic phase is an unusual first order phase
transition in which a discontinuity of the averaged order parameter appears,
even for finite number of spins. This result puts in a new way the question of
the stability of critical phenomena with respect to the long-ranged
correlations.
