Quantum Fluctuations of a 3-Dimensional φ ⁴ Model-Quantum Ferroelectrics

Abstract

A renormalization group transformation for quantum statistics is developed and applied to the φ⁴ model. We find that quantum fluctuations at T = 0 and thermal fluctuations at T ≠ 0 restore the symmetry giving rise to a ferroelectric-para-electric transition. The renormalized mass (the inverse dielectric susceptibility) and the coupling constant become temperature dependent. The renormalization constants and the Wilson functions are given by the calculation at T = 0. The inverse susceptibility for n = 1 and d = 3 (n being the number of components of the order parameter and d the dimension) is given by ${\chi^{{ - 1}}} \sim \chi_{{qmf}}^{{ - 1}}{\left| {Log\,\chi_{{qmf}}^{{ - 1}}} \right|^{{ - 1/3}}}$ (qmf refers to the quantum-mean-field susceptibility in the paraelectric phase). For materials with T_C = 0 we find $\chi_{{qmf}}^{{ - 1}} \sim {T^2}$ and ${\chi^{{ - 1}}} \sim {T^2}{\left| {Log\,{T^2}} \right|^{{ - 1/3}}}$.