Log-periodic oscillations for a uniform spin model on a fractal

The model of Blume-Capel on the Sierpinski gasket is investigated within th e method of transfer matrices, where the thermodynamic functions are obtain ed after the numerical iteration of a set of discrete maps. The analysis of the T=0 transition shows that, for antiferromagnetic coupling; and a finit e interval of self-energy coefficient, the correlation length diverges as e xp(J(eff)/T), with superimposed log-periodic oscillations in terms of the r educed temperature t=exp(-\J(eff)\T). Both the period of oscillations and t he effective interaction J(eff) depend on the strength of the actual coupli ng constants. In the antiferromagnetic regime, residual entropy is found fo r three different values of the self-energy parameter. The variation of thi s parameter leads, in the case of ferromagnetic coupling, to a more complex behavior for the correlation length than the already known exp[exp(J(eff)/ T)] dependence observed for the Ising and Potts models.