Can universality be extended to Potts antiferromagnets?1

It is well known that critical phenomena can be classified into universality classes. Ferromagnetic spin systems usually enjoy universality: these classes only depend on the spatial dimensionality of the system, and on the symmetries of the order parameter; but not on the detailed structure of the lattice. However, the less-known critical properties of antiferromagnetic spin systems usually depend on the structure of the lattice, so they should be studied on a case-by-case basis. In this talk, I consider two aspects of the phase diagram of antiferromagnetic Potts models for which some sort of universality can be recovered: (1) the parameter q_c(L) such that the q-state Potts antiferromagnet on a lattice L is always disordered at all temperatures if q>q_c(L), and it displays a zero-temperature critical point if q=q_c(L) (and is disordered at any positive temperature); and (2) the Berker-Kadanoff phase, which enjoys some intriguing properties.