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We study a Phase-Field-Crystal model described by a free energy functionalinvolving second order derivatives of the order parameter in a periodic settingand under a fixed mass constraint. We prove a $\Gamma$-convergence result in anasymptotic thin-film regime leading to a reduced 2-dimensional model. For thereduced model, we prove necessary and sufficient conditions for the globalminimality of the uniform state. We also prove similar results for theOhta-Kawasaki model.

Dimension reduction and optimality of the uniform state in a Phase-Field-Crystal model involving a higher order functional