Application of the cluster variation method to wave-number dependent susceptibility for KDP-type ferroelectrics

The cluster variation method (CVM) in the cactus approximation is applied to a pseudo-spin Ising Hamiltonian of the Slater-Takagi model for KDP-type hydrogen-bonded ferroelectrics to calculate the wave-number dependent susceptibility. After a microscopic Landau-Ginzburg variational free energy is constructed, the wave-number dependent susceptibility is derived from an equation of state obtained as the thermodynamic equilibrium condition under an inhomogeneous electric field. A strong suppression of fluctuations along the easy (z) axis is shown to appear as the ice-rule limit is approached. Though the present method is different from that of Havlin ct al., the remarkable resemblance can be seen in both expressions of susceptibility.