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Physical Review Letters

Simple Derivation of the Baxter-Model Free Energy

R. Shankar

Published Oct 26, 1981• 27 citations
Publisher

Abstract

Starting with some observations due to A. B. Zamolodchikov, a short cut to the determination of the Baxter (eight-vertex) -model free energy is developed. The method involves factorizable $S$ matrices in 1 + 1 dimensions, which are briefly reviewed. If the method generalizes, we may associate with each known $S$ matrix a Baxter-like model with a known free energy.

DOI
10.1103/physrevlett.47.1177

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Journal of Physics A Mathematical and General•Jul 21, 1990•0 citations
Starting with some observations due to A. B. Zamolodchikov, a short cut to the determination of the Baxter (eight-vertex) -model free energy is developed. The method involves factorizable SSS matrices in 1 + 1 dimensions, which are briefly reviewed. If the method generalizes, we may associate with each known SSS matrix a Baxter-like model with a known free energy.
The Yang-Baxter-Zamolodchikov-Faddeev (YBZF) algebras and their many applications are the subject of this reivew. I start by the solvable lattice statistical models constructed from YBZF algebras. All two-dimensional integrable vertex models follow in this way and are solvable via Bethe Ansatz (BA) and their generalizations. The six-vertex model solution and its q(2q−1) vertex generalization including its nested BA construction are exposed. YBZF algebras and their associated physical models are classified in terms of simple Lie algebras. It is shown how these lattice models yield both solvable massive quantum field theories (QFT) and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. The method of finite-size calculations from the BA is described as well as its applications to derive the conformal properties of integrable lattice models. It is conjectured that all integrable QFT and conformal models follow in a scaling limit from these YBZF algebras. A discussion on braid and quantum groups concludes this review.