Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

The q-state Potts model with long-range interactions that decay as 1/r(alpha) subjected to a uniform magnetic field on d-dimensional lattices is analyzed for different values of q in the nonextensive regime 0 less than or equal to alpha less than or equal to d. We calculate the mean-field solution of the model for all q and performed, for some values of q, Monte Carlo simulations for the spontaneous magnetization in the one-dimensional case. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behavior, both types of calculations present an excellent agreement for 0 less than or equal to alpha < d. We also consider the two-dimensional antiferromagnetic Ising model with competing antiferromagnetic long-range interactions and ferromagnetic first neighbor ones in the presence of a uniform magnetic field. We calculate the mean-held magnetization for this case and compare it with Monte Carlo numerical data from Sampaio et al. They also show a very good agreement for alpha<d. These results, together with some previous ones, led us to conjecture that the mean-field theory is exact for nonextensive classical spin models with 0 less than or equal to alpha < d.