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

Abstract

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 Tc : for T.Tc they are almost pure sinusoidal, while, for T,Tc , a second harmonic to the fundamental frequency is clearly observed.