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. The entropy nonextensivity is a way to introduce long-range correlations in the system. We show that for repulsive correlations, a new weak-ferromagnetic phase develops in the spin system, in addition to standard paramagnetic and ferromagnetic phases. 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.