Lectures on the integrability of the six-vertex model. (English) Zbl 1202.82022

Reshetikhin, N.

Jacobson, Jesper (ed.) et al., Exact methods in low-dimensional statistical physics and quantum computing. École d’été de Physique des Houches, session LXXXIX, 30 June–1 August 2008, école thématique du CRNS. Oxford: Oxford University Press (ISBN 978-0-19-957461-2/hbk). 197-266 (2010).

From the introduction: The goal of these notes is to outline the relation between solvable models in statistical mechanics, and classical and quantum integrable spin chains. The main examples are the six-vertex model in statistical mechanics, and spin chains related to the loop algebra \(Lsl_2\).
For the entire collection see [Zbl 1192.81012].

MSC:

82B20	Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B23	Exactly solvable models; Bethe ansatz
82B27	Critical phenomena in equilibrium statistical mechanics
17B63	Poisson algebras

Keywords:

six-vertex model; integrable spin chain; Yang-Baxter equation; quantum Lax operator; Bethe vectors; free energy