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Three-dimensional-random-site-Ising-model (3D-RSIM) along with Glauberdynamics of pseudo-spins (PSs) is applied for the first time to study therelaxion-ferroelectric-phase-transition (RFPT) ofperovskite-relaxor-ferroelectrics (PRFEs) in detail. To solve this model, weproposed a new method, mean-field of PS-strings (MF-PSSs). We find: 1) 3D-RSIMis a mixed system consisting of permanent-paraelectric-subsystem (PPSS),low-transition-temperature ferroelectric-subsystem (LTT-FSS), andhigh-transition-temperature ferroelectric-subsystem (HTT-FSS). The contents ofthese three subsystems change with the PS concentration (phi) of the model; 2)When phi < phi_p (phi_p is the percolation threshold of the 3D-RSIM), HTT-FSSdominates the whole system. On cooling, the system undergoes aninhomogeneous-diffuse-ferroelectric-phase-transition (IDFPT), and as phiincreases, it shows a crossover from the critical, gradually to Vogel-Fulcher,and to Arrehnius type slowdown. Specifically, we observe this crossover fromthe relationship between the peak temperature (Tm) of the real susceptibilityof the correlated relaxation of PSs and angular frequency (omega); 3) When phi= phi_p, the three subsystems have comparable contents. However, as temperaturedecreases, the spontaneous polarization and specific heat of the whole systemshow an IDFPT, but Tm shifts to lower temperature with omega until 0K. Sincethe relaxation time of PPSS rapidly increases at lower temperature and divergesat 0K, during a cooling process at a limited rate, PPSS must be frozen at acertain temperature, i.e. PS glass transition occurs. In short, with theincrease of phi, 3D-RSIGM gradually evolves from the IDFPT system to PS glasssystem, and phi_p is the characteristic concentration of this evolution.Moreover, based on the coupling between PSs and crystal lattice, we also give anew possible mechanism of Burns transformation.

Modeling the Ferroelectric Phase Transition in Perovskite Relaxors and New Corresponding Solving Method