Nonextensivity and Tsallis statistics in magnetic systems

We have studied the role of long-range interactions on the thermodynamics of magnetic systems. We have simulated, through the Monte Carlo method, magnetization curves of a two-dimensional classical Ising model including a long-range dipole-dipole-like interaction, where the range of interaction is tuned by a parameter {α}. Based on the conjectures of Tsallis statistics, we show that, for {α}/d{}1 (d=2), the appropriate form of the equation of state is given by M/N=m(T*,H*) with T*{≡}T/N* and H*{≡}H/N*. The normalization factor N*[N*{≡}(N^(1-α/d)-1)/(1-{α}/d)] emerges from the nonextensivity of thermodynamic variables of energy type. The crossover from nonextensive to extensive behavior at {α}/d=1 occurs smoothly and similarly to other quite different systems, thus suggesting it to be a general result.