To Critical Dynamics Near Structural Phase Transitions in Ferroelectrics: Central-Mode And Soft-Mode Behavior

Abstract

We analyze the critical dynamics of the order-disorder phase transition through the pseudo-spin quantum and classical Ising models. The findings derived by the Green-function equation-motion method and realized through Tyablikov's and Tserkovnikov's schemes, on the one hand, and the Thompson–Silva renormalization group approach, on the other hand are discussed. The slowing-down Δ and the dynamical z critical exponents are predicted for the relaxation (Δ=5/4, z=2) and resonant (Δ=5/16, z=1/2) motion regimes for three-dimensional Ising models. The results obtained give support to the idea that the classical and quantum d=2, 3 Ising models at nonzero critical temperature belong to the same universality class.