Order–Disorder and Displacive Transitions in a Quantum Ising Model

Abstract

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.

Hydrogen Atom of KH2AsO4 Determined by Neutron Diffraction Study

“…It is sometimes meaningless to distinguish between the quantum Ising and the quasi-harmonic cases. 16) It is widely accepted that the proton tunneling motion is coupled with the displacing motion of K and PO 4 in KDP-type crystals. 17) In order to explain the T c -pressure phase diagram, the mass of the quantum particle is estimated not as the proton mass but as the effective one, which is about half the mass of the H 2 PO 4 molecule.…”

Phase Diagram of Modulated Structures in Ferroelectric Crystals Based on Quantum Ising Model with Third-Neighbor Interactions

“…In appears below 62 K. 32) The dielectric susceptibility shows a broad peak at around 5 K, but no ferroelectricity is observed down to 1.5 K. [33][34][35] Such dielectric behavior is similar to the famous quantum paraelectricity in SrTiO 3 , where ferroelectricity is suppressed by quantum fluctuation. 10,11,36) While a ferroelectric transition is induced by the instability of a zone-center optical mode, the stability of a modulated structure is of concern in the general wave number q in incommensurate crystals. To explain the incommensurate phase that survives down to low temperature, we should consider third-neighbor interactions and quantum effect.…”

“…It is found that the quantum character becomes real if the energy gap of the two quantum states is comparable to the interaction energy between neighboring cells. 36) In our previous paper, only ferroic transition is treated; here, we derive the expressions of the free energy for modulated structures as well.…”

Dielectric susceptibility of quantum Ising model: Simulated monoclinic A2BX4-type ferroelectrics

“…representative of the energy gap of the single-particle Hamiltonian. 21,32) The Boltzmann constant kB is set to 1, hereafter.…”

“…Firstly, a lattice Hamiltonian including an unharmonic self-potential is presented after the model of previous works. 3,21,32,40) A quantum two-level approximation and the mean field approximation reduce the Hamiltonian to the quantum ANNNI model. Although the free energy of the quantum ANNNI model was presented previously, we briefly summarize the formulation in the next section.…”