On the Order Parameter of the Continuous Phase Transition in the Classical and Quantum Mechanical limits

The mean field theory is revisited in the classical and quantum mechanical limits. Taking into account the boundary conditions at the phase transition and the third law of the thermodynamics the physical properties of the ordered and disordered phases were reported. The equation for the order parameter predicts the occurrence of a saturation of $\Psi^2$ = 1 near $\Theta_S$, the temperature below the quantum mechanical ground state is reached. The theoretical predictions are also compared with high resolution thermal expansion data of SrTiO$_{\text{3}}$ monocrystalline samples and other some previous results. An excellent agreement has been found suggesting a universal behavior of the theoretical model to describe continuous structural phase transitions.