Relaxation dynamics near ferroelectric phase transitions and the central-peak phenomenon

The instability of the paraelectric phase in ferroelectrics, driven by ther mal fluctuations, is discussed on the basis of the quantum three-dimensiona l spin-1/2 transverse-field Ising model (TIM) within the framework of the G reen function method. The two-step critical dynamics of the TIM is analyzed through the ferroelectric order-parameter fluctuation spectra observed abo ve the critical temperature T-c. The spectra profiles are given near T-c in explicit form. The slow-down exponents Delta (c) = and 5/4 and Delta (s) = 1/4 are deduced for the slow and fast parts of structural relaxation and a re compared with those known from the literature.