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A complete proof that square ice entropy is $\tfrac 32\log _{2} (4/3)$

Part of: Equilibrium statistical mechanics Ergodic theory

Published online by Cambridge University Press:  28 April 2022

SILVÈRE GANGLOFF
SILVÈRE GANGLOFF*
Affiliation:
Faculty of Applied Mathematics of AGH, Mickiewicza, A-3/A-4, Krakow, Poland
*
e-mail: sgangloff@agh.edu.pl
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Abstract

In this text, we provide a fully rigorous and complete 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 $\tfrac 32\log _{2} (4/3)$.

Keywords

entropysquare icesix-vertex model

MSC classification

Primary: 37A35: Entropy and other invariants, isomorphism, classification
Secondary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 6 , June 2023 , pp. 1847 - 1908
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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