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 ct. Based on the conjectures of Tsallis statistics, we show that, for alpha/d less than or equal to 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-alpha/d)-1)/(1-alpha/d)] emerges from the nonextensivity of thermodynamic variables of energy type. The crossover from nonextensive to extensive behavior at alpha/d=1 occurs smoothly and similarly to other quite different systems, thus suggesting it to be a general result.