Sine-Gordon description of the scaling three-state Potts antiferromagnet on the square lattice

Abstract

The scaling limit as T->0 of the antiferromagnetic three-state Potts model on the square lattice is described by the sine-Gordon quantum field theory at a specific value of the coupling. We show that the correspondence follows unambigously from an analysis of the sine-Gordon operator space based on locality, and that the scalar operators carrying solitonic charge play an essential role in the description of the lattice model. We then evaluate the correlation functions within the form factor approach and give a number of universal predictions that can be checked in numerical simulations.

10 pages, latex

Cited by in corpus (8)

• Parafermionic conformal field theory on the lattice
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Classifying Potts critical lines
• Level spectroscopy of the square-lattice three-state Potts model with a ferromagnetic next-nearest-neighbor coupling
• Phase Diagram of the Square-Lattice Three-State Potts Antiferromagnet with Staggered Polarization Field
• On the fermion-boson correspondence for correlation functions of disorder operators
• Critical points in coupled Potts models and correlated percolation
• On the $R{P}^{N-1}$ and $C{P}^{N-1}$ universality classes