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The Yang-Baxter equations and the Zamolodchikov model. (English) Zbl 0603.58051

A summary is given of the significance of the star-triangle, or Yang- Baxter, equations in the solution of two-dimensional statistical mechanical models. The extension to the three-dimensional tetrahedron relations is quoted and it is shown how this can be used to obtain the partition function of the Zamolodchikov model for an \(n\times \infty \times \infty\) lattice. The \(n=\infty\) result differs from that recently obtained by Bazhanov and Stroganov.

MSC:

58J90 Applications of PDEs on manifolds
81T08 Constructive quantum field theory
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
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