A proof that square ice entropy is $\frac{3}{2} \log_2 (4/3)$

TL;DR

This paper provides a rigorous, detailed proof confirming that the topological entropy of square ice is exactly frac{3}{2} \, \log_2(4/3), consolidating dispersed arguments in the literature.

Contribution

It offers a complete, self-contained proof of Lieb's entropy formula for square ice, clarifying and completing previous partial arguments.

Findings

Confirmed the entropy value as frac{3}{2} \, \log_2(4/3)

Unified and detailed previous dispersed proofs

Strengthened the mathematical foundation of square ice entropy

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 $\Delta=1/2$) is equal to $\frac{3}{2}\log_2 (4/3)$. 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.