Specific heat anomalies of non-interacting fermions with multifractal energy spectra

In this work, we compute the specific heat of a system of non-interacting fermions whose energy spectrum presents a self-similar character. The critical attractor of the logistic map is used to generate a multifractal energy spectrum. We study the temperature dependence of the specific heat for distinct band fillings. At low temperatures the specific heat presents anomalies which evolve from log-periodic oscillations at low band fillings to more complex patterns which strongly depends on the actual position of the Fermi energy. We relate the character of these anomalies with some scaling exponents which characterize the discrete scale invariance of the energy spectrum.