The Ferromagnetic Potts model under an external magnetic field: an exact renormalization group approach

TL;DR

This paper presents an exact real-space renormalization group analysis of the q-state ferromagnetic Potts model under an external magnetic field on fractal lattices, revealing complex critical phenomena including Potts and Ising-like transitions.

Contribution

It introduces an exact RG approach for the Potts model with a magnetic field on fractal lattices, uncovering novel critical behaviors and phase transitions.

Findings

Identified Potts criticality at zero field.

Discovered Ising-like phase transition under strong reverse magnetic field.

Observed cusps and dimensional reduction on the critical surface.

Abstract

The q-state ferromagnetic Potts model under a non-zero magnetic field coupled with the 0^th Potts state was investigated by an exact real-space renormalization group approach. The model was defined on a family of diamond hierarchical lattices of several fractal dimensions d_F. On these lattices, the renormalization group transformations became exact for such a model when a correlation coupling that singles out the 0^th Potts state was included in the Hamiltonian. The rich criticality presented by the model with q=3 and d_F=2 was fully analyzed. Apart from the Potts criticality for the zero field, an Ising-like phase transition was found whenever the system was submitted to a strong reverse magnetic field. Unusual characteristics such as cusps and dimensional reduction were observed on the critical surface.