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Scaling Laws for a System with long-range Interactions within Tsallis statistics

Salazar, Rafael; Toral, Raul;
Physical Review Letters 83, 4233-4236 (1999)

We study the one-dimensional Ising model with long-range interactions in the context of Tsallis non-extensive statistics by computing numerically the number of states with a given energy. We find that the internal energy, magnetization, entropy and free energy follow non-trivial scaling laws with the number of constituents N and temperature T. Each of the scaling functions for the internal energy,the magnetization and the free energy, adopts three different forms corresponding to q>1, q=1 and q<1, being q the non-extensivity parameter of Tsallis statistics.
(2 pages, 3 figures, LaTeX, postscript version here).