The Transverse Ising Model of the Ferroelectric Phase Transition in a System of Coupled Small Particles

Abstract

The transverse Ising model was developed for an array of coupled ferroelectric small particles. Two contributions to exchange integral were included: dipole-dipole interaction and short-range coupling. General analytical equations were found for the ferroelectric phase transition temperature and order parameter. The equations obtained were analyzed numerically for cubic and tetragonal lattices of particles and cells. The shift of the ferroelectric phase transition temperature was considered as a function of the interparticle distance, tunneling constant, and geometry of particle arrangement.

Keywords:

• Array of coupled small ferroelectric particles
• Ising model
• tunneling
• shift of the phase transition temperature
• dipole-dipole and short-range couplings