Loss of elastic stability and formation of inhomogeneous states at phase transitions in thin films on substrates

Within the Landau-like approach we study stability of homogeneous states near phase transitions in thin films on substrates. The order parameter is electrically neutral in order to exclude the effects of the depolarizing fields and concentrate on the elasticity effects. We consider the case where the first-order transition in free crystal would convert into a second order when in the film on a substrate if the system remained homogeneous. Limit of stability of the homogeneous state is found analytically, though approximately. Numerical simulations provide qualitatively similar results and reveal temperature evolution of the arising inhomogeneities.