Currently used methods for the description of thermodynamics of ferroelectric
thin films (Landau theory or ab initio based Monte-Carlo simulations) are based
on an energy expansion in terms of internal degrees of freedom. It was shown
that these methods can suffer from a substantial inaccuracy unless higher-order
electromechanical interactions are not taken into account. The high-order
electromechanical couplings strongly renormalize the sixth-power polarization
terms of the thermodynamic energy expansion. In this paper, apart from the
general statement, we illustrate it with an example of a temperature - misfit
strain phase diagram of a BaTiO3 thin film derived with high-order
electromechanical interactions evaluated using first principles calculations