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Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces
Andrew P. Kels
The new concept of a system of hex equations is introduced as an overdetermined system of six five-point face-centered quad equations defined on six vertices of a hexagon. For a co…
Interaction-round-a-face and consistency-around-a-face-centered-cube
Andrew P. Kels
There is a correspondence between integrable lattice models of statistical mechanics and discrete integrable equations which satisfy multidimensional consistency, where the latter…
Extended Z-invariance for integrable vector and face models and multi-component integrable quad equations
Andrew P. Kels
In a previous paper, the author has established an extension of the Z-invariance property for integrable edge-interaction models of statistical mechanics, that satisfy the star-tri…
Integrable quad equations derived from the quantum Yang-Baxter equation
Andrew P. Kels
This paper presents an explicit correspondence between two different types of integrable equations; the quantum Yang-Baxter equation in its star-triangle relation form, and the cla…