STUDY OF THE MEAN-FIELD RENORMALIZATION-GROUP METHOD WITH THE TSALLISSTATISTICS

The phase transition of the Ising model in d-dimensional lattice is re analyzed by using the mean field renormalization group method within t he Tsallis generalization of the Boltzmann-Gibbs statistics (BGS). The critical temperature (T-c) is obtained explicitly for a general dimen sion d and a factor q present in the generalized statistics for cluste rs of one (N' = 1) and two (N = 2) spins. In the q --> 1 limit, the pr esent work reduces to the results of Indekeu et al. (J. Phys. A 15 (19 82) L291) with the usual BGS. For a linear chain (d = 1), the system p resents a phase transition for q not equal 1. When we have q much grea ter than 1, T-c(d,q) is proportional to the factor q, in accordance wi th the result of mean field approximation (E.F. Sarmento, Physica A 21 8 (1995) 482).