Polarization fluctuations in ferroelectric models

We consider the relation between the finite-wave-vector susceptibility $\chi \left(\overrightarrow{\mathrm{q}}\right)$ of the six-vertex model family and the macroscopic susceptibility. This is nontrivial because $\chi \left(\overrightarrow{\mathrm{q}}\right)$ is singular at $\overrightarrow{\mathrm{q}}=0\mathrm{}$. Using exact results for the macroscopic susceptibility, we infer the analytic form of the anisotropy parameter appearing in the pair-correlation function at large separation. Proceeding phenomenologically, we consider the effect of relaxing the ice rules, and the effect of short-ranged interactions other than the ice rules (e.g., polarization gradient energies).