A proof that square ice entropy is (3)/(2) log₂ (4/3)

2019/02/25 by Silvère Gangloff, Gangloff, Silvère
Computer Science · Mathematics · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1902.09274

openalex publication_date 2019/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this text, we provide a fully rigorous, complete and self-contained proof of E.H.Lieb's statement that (topological) entropy of square ice (or six vertex model, XXZ spin chain for anisotropy parameter Δ=1/2) is equal to (3)/(2)log₂ (4/3). For this purpose, we gather and expose in full detail various arguments dispersed in the literature on the subject, and complete several of them that were left partial.

Citations

• Two soluble models of an antiferromagnetic chain
• The algebraic Bethe Ansatz and combinatorial trees

Related

• Equivalence of residual entropy of hexagonal and cubic ices from tensor network methods
• Theory of the [111] magnetization plateau in spin ice
• Correlation between residual entropy and spanning tree entropy of ice-type models on graphs
• On Pauling's residual entropy estimate for regular graphs with growing degree
• A remark on entropy numbers