Order-Disorder and Displacive Transitions in a Quantum Ising Model

A ferrodistortive phase transition is analyzed for a quantum particles in a simple quartic potential. The interactions are taken into account by the mean-field approximation. A quantum thermodynamic treatment gives analytic expressions for the static susceptibility, the specific heat and the soft mode frequency. The Rhodes–Wohlfarth ratio is a measure whether the system is order–disorder or displacive, however, the border is fuzzy depending on the interaction strength. The quantum effect is discussed when the transition takes place at low temperature. Whether the atomic density is a single or multiple peak distributions seems to be a definite criterion for the character of the structural phase transition.