Abstract
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.
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