Polarization fluctuations in ferroelectric models

Abstract

We consider the relation between the finite-wave-vector susceptibility $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ of the six-vertex model family and the macroscopic susceptibility. This is nontrivial because $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ is singular at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}=0$. 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).