Exact Results for the Residual Entropy of Ice Hexagonal Monolayer

TL;DR

This paper derives exact residual entropy values for ice hexagonal monolayers under different conditions, expanding the set of exactly solvable two-dimensional ice models using mappings to Ising and six-vertex models.

Contribution

It provides the first exact residual entropy calculations for ice hexagonal monolayers in two specific scenarios, using mappings to well-known statistical models.

Findings

Residual entropy under electric field matches dimer model results

Exact entropy obtained via six-vertex model under periodic boundary conditions

Expands the class of exactly solvable 2D ice models

Abstract

Since the problem of the residual entropy of square ice was exactly solved, exact solutions for two-dimensional realistic ice models have been of interest. In this paper, we study the exact residual entropy of ice hexagonal monolayer in two cases. In the case that the external electric field along the z-axis exists, we map the hydrogen configurations into the spin configurations of the Ising model on the Kagom\'e lattice. By taking the low temperature limit of the Ising model, we derive the exact residual entropy, which agrees with the result determined previously from the dimer model on the honeycomb lattice. In another case that the ice hexagonal monolayer is under the periodic boundary conditions in the cubic ice lattice, we employ the six-vertex model on the square lattice to represent the hydrogen configurations obeying the ice rules. The exact residual entropy in this case is obtained from the solution of the equivalent six-vertex model. Our work provides more examples of the exactly soluble two-dimensional models.