Exact Solution of the Problem of the Entropy of Two-Dimensional Ice

At low temperatures ice has a residual entropy caused, presumably, by an indeterminacy of the crystal structure. The oxygen atoms constitute a periodic crystal lattice that is hydrogen bonded. The hydrogen atoms are not at the centers of the bonds, however, so that there are two possible states for each bond corresponding to the two positions of the hydrogen atom relative to the bond midpoint. Nevertheless, not all bond configurations are allowed, for there is a constraint called the “ice condition” such that for the four bonds emanating from each oxygen atom, exactly two of the bonds must have the hydrogen atoms close to the oxygen atom.