Field Theory of Scaling Lattice Models: The Potts Antiferromagnet

A. Bakchich, A. Benyoussef, M. Touzani

John Cardy, Jesper Lykke Jacobsen, Alan D. Sokal

Jesper Lykke Jacobsen, Hubert Saleur

Gesualdo Delfino

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.

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20–120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model.

Aloysius P. Gottlob, Martin Hasenbusch B