A lattice Monte Carlo study of Inverse Symmetry Breaking in a two-scalar model in three dimensions

We carry a Monte Carlo study of the coupled two-scalar $\lambda\phi^2_1 \phi^2_2$ model in three dimensions. We find no trace of Inverse Symmetry Breaking in the region of negative $\lambda$'s for which the one-loop effective potential predicts this phenomenon. Moreover, for $\lambda$'s negative enough, but still in the stability region for the potential, one of the transitions turns out to be of first order, both for zero and finite temperature.