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Mean-field theory description of structural phase transitions in a model ferroelectric with double Morse substrate potential

We investigate the general features of a ferroelectric D-dimensional hypercubic model, with a symmetric double Morse-type on-site potential and nearest-neighbour interaction, that exhibits structural phase transitions. The mean-field theory (MFT) is developed for this model where the anharmonicity is the main characteristic. It is based on making a Gaussian ansatz for the single-particle probability density function and helps us to make a more extensive survey of the order parameter. Two different cases are considered and analytical results analysed. Finally, we discuss the important features of the Hamiltonian, depending on the range of the force constant on the one hand and the strength of the anharmonicity on the other, which is responsible for these structural transitions (first order and second order).