In statistical mechanics, the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such model was introduced by Linus Pauling in 1935 to account for the residual entropy of water ice.[1] Variants have been proposed as models of certain ferroelectric[2] and antiferroelectric[3] crystals.
In 1967, Elliott H. Lieb found the exact solution to a two-dimensional ice model known as "square ice".[4] The exact solution in three dimensions is only known for a special "frozen" state.[5]