Frustrated Potts model: Multiplicity eliminates chaos via reentrance

Chaotic renormalization flow in the Potts model induced by long-range competition

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 concentrate on models with either complicated or nonrealistic interactions in order to achieve this chaotic behavior. 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 antiferromagnetic 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. These surprising and universal findings may shed light on the study of spin glass.