Abstract
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 ( T c) 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, T c( d, q) is proportional to the factor q, in accordance with the result of mean field approximation.
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