Discrete scale invariance, and its logarithmic extension
  It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and inversion, and find general forms for correlation functions. 
N. Abed-Pour, A. Aghamohammadi, M. Khorrami, M. Reza Rahimi Tabar