Renormalisation groups with periodic and aperiodic orbits

Abstract

Motivated by recent results for some frustrated hierarchical models, the authors analyse the consequences of renormalisation group transformations with periodic and aperiodic orbits. They find that the free energy has in general an infinite number of singularities. This occurs already when the transformation has a stable periodic orbit. They present an idealised example, and a new class of hierarchical Potts models to which the theory applies.