Field theory of scaling lattice models. The Potts antiferromagnet

In contrast to what happens for ferromagnets, the lattice structure participates in a crucial way to determine existence and type of critical behaviour in antiferromagnetic 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 behaviour is also introduced.Comment: 11 pages, to appear in the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 200