New Two-Dimensional Ice Models

Abstract

This paper presents a new approach for enumerating all hydrogen bond arrange- ments of ice-like systems with periodic boundary conditions. It is founded on a topological procedure for the dimensional reduction and a new variant of the transfer matrix method based on small conditional transfer matrices. We consider a couple of new two-dimensional ice models on very unusual lattices. One of them is the twisted square ice model with cross- ing H-bonds. The other is the digonal-hexagonal model with double H-bonds. In spite of their uncommonness, these models are quite realistic, because from the standpoint of com- binatorics and topology they are equivalent to the layers of usual hexagonal ice Ih under periodic boundary conditions in one of the directions. The exact proton configuration statis- tics for a number of 2D-expanded unit cells of hexagonal ice Ih and the residual entropy of the new ice models in the large system limit are presented.