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.