Renormalization Group Study Of Potts Model On Hierarchical Lattice

A proper description of spin glass remains a hard subject in theoretical physics and is considered to be closely related to the emergence of chaos in the renormalization group(RG)flow.Previous efforts propose models with either complicated or non-realistic interactions in order to achieve this chaotic behaviour.Here we find that the commonly used Potts model with long-range interaction could do the job nicely in a large parameter regime as long as the competition between the ferromagnetic and anti-ferromagnetic interaction is maintained.With this simplicity,the appearance of chaos is observed to sensitively depend on the detailed network structure:the parity of bond number in a branch of the basic RG substituting unit:chaos only emerges for even numbers of bonds.This surprising and universal finding may shed new light on the study of spin glass.