Abstract
A cluster expansion approach for the Kirkwood orientational correlation factor gk in ice has been examined. The expansion parameter measures the extent to which neighboring molecules obey bonding requirements of the ``ice rules.'' For cubic ice, leading terms have been evaluated in the series for the separate contributions to gk from the first three shells of neighbors. These series tend to confirm the validity of a recent Monte Carlo estimate of gk, but they also suggest that orientational order in cubic and hexagonal ices has long range and is analogous to local order of critical point pair correlations in Ising models. As a result, the cluster expansion for gk itself likely converges very slowly, if at all.
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