Absolute minimum of Landau’s thermodynamic potential

We present a general method for finding the absolute minimum of Landau’s thermodynamic potential. The method is illustrated in the example of the most general sixth-degree potential for a physical system whose order parameters transform as one of the three-dimensional vector representations of $O_h$, O, and $T_h$. The results are used to explain the three successive phase transitions occurring in ${\mathrm{BaTiO}}_3$. The phase-transition conditions are obtained in an analytic form. We show why the perovskite-type crystals differ vastly in phase-transition properties even though their compositions are so similar.