Antiferromagnetic four-dimensional O(4) model

We study the phase diagram of the four-dimensional O(4) model with first- (β_(1)) and second- (β2) neighbor couplings, especially in the β_(2) < 0 region, where we find a line of transitions which seems to be second order. We also compute the critical exponents on this line at the point β_(1) = 0 (F_(4) lattice) by finite-size scaling techniques up to a lattice size of 24, these exponents being different from the mean-field ones