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(${\mathrm{T}}^{\mathrm{*}}$,${\mathrm{H}}^{\mathrm{*}}$) with ${\mathrm{T}}^{\mathrm{*}}$≡T/${\mathrm{N}}^{\mathrm{*}}$ and ${\mathrm{H}}^{\mathrm{*}}$≡H/${\mathrm{N}}^{\mathrm{*}}$. The normalization factor ${\mathrm{N}}^{\mathrm{*}}$[${\mathrm{N}}^{\mathrm{*}}$≡(${\mathrm{N}}^{\left(1\mathrm{}\mathrm{-}\mathrm{\alpha }\mathrm{/}\mathrm{d}\right)}$-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.