Antiferromagnetism in four dimensions: search for non-triviality

We present antiferromagnetism as a mechanism capable of modifying substantially the phase diagram and the critical behaviour of statistical mechanical models. This is particularly relevant in four dimensions, due to the connection between second order transition points and the continuum limit as a quantum field theory. We study three models with an antiferromagnetic interaction: the Ising and the O(4) Models with a second neighbour negative coupling, and the \RP{2} Model. Different conclusions are obtained depending on the model.Comment: 4 pages LateX. Contribution to Lat9

Phase diagram of d=4 Ising Model with two couplings

We study the phase diagram of the four dimensional Ising model with first and second neighbour couplings, specially in the antiferromagnetic region, by using Mean Field and Monte Carlo methods. From the later, all the transition lines seem to be first order except that between ferromagnetic and disordered phases in a region including the first-neighbour Ising transition point.Comment: Latex file and 4 figures (epsfig required). It replaces the preprint entitled "Non-classical exponents in the d=4 Ising Model with two couplings". New analysis with more statistical data is performed. Final version to appear in Phys. Lett.