Connection between energy-spectrum self-similarity and specific heat log-periodicity

As a first step towards the understanding of the thermodynamical properties of quasiperiodic structures, we have performed both analytical and numerical calculations associated with succesive hierarchical approximations to multiscale fractal energy spectra. We show that, in a certain range of temperatures, the specific heat displays log-periodic oscillations as a function of the temperature. We exhibit scaling arguments that allow for relating the mean value as well as the amplitude and period of the oscillations to the characteristic scales of the spectrum.