Quantum tunneling versus zero-point energy in double-well potential model for ferrroelectric phase transitions

The Ising model in a transverse field, which involves quantum tunneling in double potential wells, has been used for many years to describe ferroelectric phase transitions. An alternative model previously published takes into account the effect of a non-negligible zero-point energy in the double potential wells at the phase transition. A comparison of the respective Curie temperatures, spontaneous polarizations and susceptibilities shows that both models are nearly equivalent. Quantitative differences of the two methods are apparent at low temperature where the saturation polarization value with non-negligible zero-point energy is higher than the same quantity with the Ising model in a transverse field.