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

Abstract

The model of Blume-Capel on the Sierpinski gasket is investigated within the method of transfer matrices, where the thermodynamic functions are obtained after the numerical iteration of a set of discrete maps. The analysis of the T50 transition shows that, for antiferromagnetic coupling and a finite interval of self-energy coefficient, the correlation length diverges as exp(Jef f /T), with superimposed log-periodic oscillations in terms of the reduced temperature t5exp(2uJef fu/T). Both the period of oscillations and the effective interaction Je f f depend on the strength of the actual coupling constants. In the antiferromagnetic regime, residual entropy is found for three different values of the self-energy parameter. The variation of this parameter leads, in the case of ferromagnetic coupling, to a more complex behavior for the correlation length than the already known exp@exp(Jef f /T)# dependence observed for the Ising and Potts models.