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

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... 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.