Violation of the principle of minimality of the free energy in the self-consistent field approximation for some models of ferroelectrics

For the example of a simple model used in the theory of ferroelectricity it is shown that the equilibrium values of the thermodynamic parameters cannot correspond to a minimum of the free energy in the self-consistent field approximation. This is explained by the fact that the approximate equilibrium values of the thermodynamic parameters are determined on the basis of Bogolyubov's variational principle; this principle requires minimization of not the approximate free energy itself but rather the difference between the approximate free energy and the exact free energy. If the Hamiltonian of the system contains a negative (antiferromagnetic) or positive (ferromagnetic) effective interaction, the free energy in the molecular field approximation is maximal or minimal with respect to the corresponding thermodynamic parameter.