Quantum discrete $\phi ^4$ model at finite temperatures: the mean-field phase diagram

The quantum discrete $\phi ^4$ model at finite temperature is studied in the mean-field approximation. The phase diagrams are obtained for a wide range of the model parameters. The domains of applicability for the classical, quantum, and order-disorder limits are determined. It is shown that a remarkable part of the phase diagram is reproduced by the first quantum correction to the classical result. Parameters of Sn$_2$P$_2$S$_6$, SrTiO$_3$, and KH$_2$PO$_4$ are placed in the phase diagram of the model.