4 papers
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…
Lens Generalisation of -functions for the Elliptic Discrete Painlevé Equation
Andrew P. Kels, Masahito Yamazaki
We propose a new bilinear Hirota equation for -functions associated with the root lattice, that provides a "lens" generalisation of the -functions for the elliptic disc…
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…