  The transverse Ising model (TIM), with pseudospins representing the lattice
polarization, is often used as a simple description of ferroelectric materials.
However, we demonstrate that the TIM, as it is usually formulated, provides an
incorrect description of SrTiO$_{3}$ films and interfaces because of its
inadequate treatment of spatial inhomogeneity. We correct this deficiency by
adding a pseudospin anisotropy to the model. We demonstrate the physical need
for this term by comparison of the TIM to a typical Landau-Ginzburg-Devonshire
model. We then demonstrate the physical consequences of the modification for
two model systems: a ferroelectric thin film, and a metallic
LaAlO$_{3}$/SrTiO$_{3}$ interface. We show that, in both cases, the modified
TIM has a substantially different polarization profile than the conventional
TIM. In particular, at low temperatures the formation of quantized states at
LaAlO$_{3}$/SrTiO$_{3}$ interfaces only occurs in the modified TIM.
