Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models

Abstract

We compute the action-angle coordinates for an Ising type model whose L-operator has been previously studied in the literature by Bazhanov and Sergeev. In comparison to computations with such operators that have been examined previously by the author for the 4-vertex, 6-vertex, and 20-vertex, models, computations for asymptotically approximating a collection of sixteen identities with the Poisson bracket, which together constitute the Poisson structure of the Ising type model, exhibit dependencies upon nearest neighbor interactions. Inspite of the fact that L-operators for the 20-vertex model are defined in terms of combinatorial, and algebraic, constituents unlike such operators for the 6-vertex model which are defined in terms of projectors and Pauli basis elements, L-operators for the Ising-type model can be used for concluding that a model which interpolates between the 6-vertex, and 8-vertex, models is exactly solvable.

Template (114 pages). Related topics of discussion are at: https://youtu.be/tIO0AwbQp6Q, https://youtu.be/93KhYI8Fy_M, https://youtu.be/PQBB5ENUO-g, https://youtu.be/P1EF54ZF84s, https://youtu.be/SHYwtt81Q3E, https://youtu.be/LM9xakHYAog, https://youtu.be/sdfYV6ESEe8