Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2000-08-14
Physica A 360, 365-378 (2006)
Physics
Condensed Matter
Disordered Systems and Neural Networks
10 pages, 7 figures, 3 Tables, 17 references
Scientific paper
10.1007/s100510170057
The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierachical lattices is investigated. The geometric fluctuations are introduced by generalized Fibonacci sequences. The local magnetization is evaluated via an exact recurrent procedure encompassing a real space renormalization group decimation. The symmetries of the local magnetization patterns induced by the aperiodic couplings is found to be strongly (weakly) different, with respect to the ones of the corresponding homogeneous systems, when the geometric fluctuations are relevant (irrelevant) to change the critical properties of the system. At the criticality, the measure defined by the local magnetization is found to exhibit a non-trivial F(alpha) spectra being shifted to higher 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.
Edvaldo Nogueira Jr.
Andrade Roberto F. S.
Coutinho Sérgio
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