Log-periodic corrections to scaling: exact results for aperiodic Ising   quantum chains
  Log-periodic amplitudes of the surface magnetization are calculated analytically for two Ising quantum chains with aperiodic modulations of the couplings. The oscillating behaviour is linked to the discrete scale invariance of the perturbations. For the Fredholm sequence, the aperiodic modulation is marginal and the amplitudes are obtained as functions of the deviation from the critical point. For the other sequence, the perturbation is relevant and the critical surface magnetization is studied. 
Dragi Karevski and Loic Turban (Henri Poincare, Nancy I)