Multifractal properties of aperiodic Ising model on hierarchical lattices:role of the geometric fluctuations

The role of the geometric fluctuations on the multifractal properties of th e local magnetization of aperiodic ferromagnetic Ising models on hierarchic al lattices is investigated. The geometric fluctuations are introduced by g eneralized Fibonacci sequences. The local magnetization is evaluated via an exact recurrent procedure encompassing real space renormalization group de cimation. The symmetries of the local magnetization patterns induced by the aperiodic couplings is found to be strongly (weakly) different, with respe ct to the ones of the corresponding homogeneous systems, when the geometric fluctuations are relevant (irrelevant) to change the critical properties o f the system. At the criticality, the measure defined by the local magnetiz ation is found to exhibit a non-trivial F(alpha) spectra being shifted to h igher values of alpha when relevant geometric fluctuations are considered. The critical exponents are found to be related with some special points of the F(alpha) function and agree with previous results obtained by the quite distinct transfer matrix approach.