New integrable lattice models from Fuss-Catalan algebras |
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| Affiliation: | 1. Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, N.C. 27599-3250, USA;2. Service de Physique Théorique, C.E.A. Saclay, F-91191 Gif-sur-Yvette Cedex, France;1. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile;2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile;1. College of Education for the Future, Beijing Normal University, Zhuhai 519087, China;2. Department of Physics, Beijing Normal University, Beijing, 100875, China;1. Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, 14476, Potsdam, Germany;2. Tamm Department of Theoretical Physics, Lebedev Physical Institute, Leninsky prospekt 53, 119991, Moscow, Russia |
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| Abstract: | We construct new hyperbolic solutions of the Yang-Baxter equation, using the Fuss-Catalan algebras, a set of multi-colored versions of the Temperley-Lieb algebra, recently introduced by Bisch and Jones. These lead to new two-dimensional integrable lattice models, describing dense gases of colored loops. |
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