ANTIFERROMAGNETISM IN 4 DIMENSIONS - SEARCH FOR NONTRIVIALITY

We present antiferromagnetism as a mechanism capable of modifying subs tantially the phase diagram and the critical behaviour of statistical mechanical models. This is particularly relevant in four dimensions, d ue to the connection between second order transition points and the co ntinuum limit as a quantum field theory. We study three models with an antiferromagnetic interaction: the Ising and the O(4) Models with a s econd neighbour negative coupling, and the RP(2) Model. Different conc lusions are obtained depending on the model.