  The time dependent cluster approximation called the path probability method
(PPM) is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model
for KH2PO4-type hydrogen-bonded ferroelectrics in order to calculate the
homogeneous dynamical susceptibility above and below the ferroelectric
transition temperature. Above the transition temperature all the calculations
are carried out analytically in the cactus approximation of the PPM. Below the
transition temperature the dynamical susceptibility is also calculated
accurately since the analytical solution of spontaneous polarization in the
ferroelectric phase can be utilized. When the temperature is approached from
both sides of the transition temperature, only one of relaxation times shows a
critical slowing down and makes a main contribution to the dynamical
susceptibility. The discrepancy from Slater model (ice-rule limit) is discussed
in comparison with some experimental data.
