Colouring Solutions of the Ice Problem

Abstract

The ice problem on a lattice can be expressed in terms of arrow configurations on bonds with equal numbers of arrows pointing to and away from the vertices. In some cases vertex (ice) models can be expressed as colouring problems. We use the colouring association in conjunction with an old heuristic argument of Pauling to (re)derive the exact results for the residual entropy of ice on the square and triangular lattices. © 2011 Springer Science+Business Media, LLC.