FIELD THEORY OF SCALING LATTICE MODELS: THE POTTS ANTIFERROMAGNET

摘要

In contrast to what happens for ferromagnets, the lattice structure participates in a crucial way to determine existence and type of critical behavior in antiferro-magnetic systems. It is an interesting question to investigate how the memory of the lattice survives in the field theory describing a scaling antiferromagnet. We discuss this issue for the square lattice three-state Potts model, whose scaling limit as T→0 is argued to be described exactly by the sine-Gordon field theory at a specific value of the coupling. The solution of the scaling ferromagnetic case is recalled for comparison. The field theory describing the crossover from antiferromagnetic to ferromagnetic behavior is also introduced.