  Three-dimensional-random-site-Ising-model (3D-RSIM) along with Glauber
dynamics of pseudo-spins (PSs) is applied for the first time to study the
relaxion-ferroelectric-phase-transition (RFPT) of
perovskite-relaxor-ferroelectrics (PRFEs) in detail. To solve this model, we
proposed a new method, mean-field of PS-strings (MF-PSSs). We find: 1) 3D-RSIM
is a mixed system consisting of permanent-paraelectric-subsystem (PPSS),
low-transition-temperature ferroelectric-subsystem (LTT-FSS), and
high-transition-temperature ferroelectric-subsystem (HTT-FSS). The contents of
these 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-FSS
dominates the whole system. On cooling, the system undergoes an
inhomogeneous-diffuse-ferroelectric-phase-transition (IDFPT), and as phi
increases, it shows a crossover from the critical, gradually to Vogel-Fulcher,
and to Arrehnius type slowdown. Specifically, we observe this crossover from
the relationship between the peak temperature (Tm) of the real susceptibility
of the correlated relaxation of PSs and angular frequency (omega); 3) When phi
= phi_p, the three subsystems have comparable contents. However, as temperature
decreases, the spontaneous polarization and specific heat of the whole system
show an IDFPT, but Tm shifts to lower temperature with omega until 0K. Since
the relaxation time of PPSS rapidly increases at lower temperature and diverges
at 0K, during a cooling process at a limited rate, PPSS must be frozen at a
certain temperature, i.e. PS glass transition occurs. In short, with the
increase of phi, 3D-RSIGM gradually evolves from the IDFPT system to PS glass
system, and phi_p is the characteristic concentration of this evolution.
Moreover, based on the coupling between PSs and crystal lattice, we also give a
new possible mechanism of Burns transformation.
