  We study a Phase-Field-Crystal model described by a free energy functional
involving second order derivatives of the order parameter in a periodic setting
and under a fixed mass constraint. We prove a $\Gamma$-convergence result in an
asymptotic thin-film regime leading to a reduced 2-dimensional model. For the
reduced model, we prove necessary and sufficient conditions for the global
minimality of the uniform state. We also prove similar results for the
Ohta-Kawasaki model.
