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

Fuente: arXiv
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Autore principale: Rigas, Pete
Natura: Preprint
Pubblicazione: 2024
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author Rigas, Pete
author_facet Rigas, Pete
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_01996
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models
Rigas, Pete
Statistical Mechanics
Mathematical Physics
Probability
Exactly Solvable and Integrable Systems
34L25, 60K35
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.
title Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models
topic Statistical Mechanics
Mathematical Physics
Probability
Exactly Solvable and Integrable Systems
34L25, 60K35
url https://arxiv.org/abs/2501.01996