Renormalization by substitution on 2-D Potts models
G. Albinet, H. Ottavi · Journal de physique · 1986
A new renormalization method in position space (renormalization by substitution) that can be applied to some two-dimensional lattices is described in the framework of Potts model on Kagomé and on triangular lattices. Unfortunately the transformation thus defined is not injective and one must find a criterion to eliminate this difficulty : this problem is solved with the aid of the Julia set associated with the transformation. Critical temperatures are obtained, which are in better agreement with the exact results than those obtained with the Migdal-Kadanoff approximation ; critical exponents are also improved, but in a less spectacular manner.