Detailed characterization of log-periodic oscillations for an aperiodic Ising model

This work analyzes the behavior of Ising spins on a hierarchical lattice subject to relevant fluctuations on the coupling constants induced by a deterministic aperiodic sequence, The thermodynamical functions are evaluated within the method of transfer matrices. It is shown that log-periodic oscillations in the reduced temperature are present for all thermodynamical functions close to the critical point and that the nature of oscillations changes discontinuously at T-c: for T>T-c they are almost purr sinusoidal, while, fur T<T-c, a second harmonic to the fundamental frequency is clearly observed.