2026-06-26T02:56:03Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/515492023-08-27T05:26:48Zcom_20.500.14352_14col_20.500.14352_15

Solvable scalar and spin models with near-neighbors interactions Enciso, A. Finkel Morgenstern, Federico González López, Artemio Rodríguez González, Miguel Ángel ©2004 Elsevier B.V. This work was partially supported by the Spanish DGI under grant No. BFM2002-02646. A.E. acknowledges the financial support of the Spanish Ministry of Education through an FPU scholarship We construct new solvable rational and trigonometric spin models with near-neighbors interactions by an extension of the Dunkl operator formalism. In the trigonometric case we obtain a finite number of energy levels in the center of mass frame, while the rational models are shown to possess an equally spaced infinite algebraic spectrum. For the trigonometric and one of the rational models, the corresponding eigenfunctions are explicitly computed. We also study the scalar reductions of the models, some of which had already appeared in the literature, and compute their algebraic eigenfunctions in closed form. In the rational cases, for which only partial results were available, we give concise expressions of the eigenfunctions in terms of generalized Laguerre and Jacobi polynomials. 2023-06-20T10:58:53Z 2023-06-20T10:58:53Z 2005-01-06 journal article 0370-2693 10.1016/j.physletb.2004.11.031 https://hdl.handle.net/20.500.14352/51549 http://dx.doi.org/10.1016/j.physletb.2004.11.031 http://www.sciencedirect.com eng BFM2002-02646 FPU scholarship https://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España Elsevier Science BV