Type I FCC antiferromagnets in a magnetic field: a realisation of the q=3- and q=4-state Potts models

It is suggested that phase transitions induced by a magnetic field H//(111) in certain type I FCC antiferromagnets provide a physical realisation of the q=3- and q=4-state Potts models. The (H, T) phase diagram associated with these antiferromagnets for a field lying in the (110) plane is studied using mean field approximation and renormalisation group calculations in d=- epsilon dimensions. The phase diagram exhibits a critical and two first-order surfaces connected by lines to tricritical and polycritical points.