Entropy of hard hexagons

Abstract

Metcalf and Yang (1978) have obtained the numerical estimate 0.3333 k for the entropy per site of hard hexagons. They therefore conjecture that the exact value is k/3. The authors have used the corner transfer matrix method to obtain a more accurate numerical estimate, namely 0.333 242 721 976 k, which contradicts the conjecture. The problem is a good example of the numerical accuracy of the method.