Specific heat log-periodicity from multifractal energy spectra

In this work, we investigate the emergence of log-periodic oscillations in the low-temperature behavior of the specific heat of systems whose energy spectra present a self-similar character. The critical attractor of z-generalized logistic maps are used to generate multifractal energy spectra with tunable singularity spectra. We study the relationship between the average value and amplitude of the log-periodic oscillations on the map nonlinearity strength as well as on the scaling exponents characterizing the energy spectrum. Our numerical results show a monotonic decrease of the oscillations amplitude with increasing nonlinearity. Further, we obtain that the average low-temperature specific heat is directly related to the minimum singularity strength governing the scaling behavior of the most concentrated energy range. (C) 2003 Elsevier B.V. All rights reserved.