The transverse Ising model is considered in the static fluctuation approxim
ation. This hinges on the replacement of the local field operator with its
mean value; only the quadratic fluctuations of the local held are retained.
The model is applied to ferroelectrics of the order-disorder type, such as
monoaxial crystalline threeglycinsulfate. Analytic expressions are derived
for the spontaneous polarization, the specific heat, the pair correlation
function, and the static susceptibility of this ferroelectric. Its main cha
racteristics are then determined numerically as functions of the temperatur
e. In particular, its critical behavior is obtained automatically for a spe
cific value of some "control" parameter. It is predicted that, with respect
to this parameter, the specific heat exhibits a logarithmic behavior to th
e right of the critical point; this is interpreted as a consequence of the
long range and axial anisotropy of the dipole-dipole interaction. In passin
g, the behavior of the lattice Green function for the anisotropic dipole-di
pole potential near the critical point is thoroughly examined.