Study of the mean field renormalization group method with the Tsallis statistics

The phase transition of the Ising model in d-dimensional lattice is reanalyzed by using the mean field renormalization group method within the Tsallis generalization of the Boltzmann-Gibbs statistics (BGS). The critical temperature (Tc) is obtained explicitly for a general dimension d and a factor q present in the generalized statistics for clusters of one (N′ = 1) and two (N = 2) spind. In the q → 1 limit, the present work reduces to the results of Indekeu et al. (J. Phys. A 15 (1982) L291) with the usual BGS. For a linear chain (d = 1), the system presents a phase transition for q ≠ 1. When we have q 1, Tc(d,q) is proportional to the factor q, in accordance with the result of mean field approximation.