Publication: Solvable scalar and spin models with near-neighbors interactions
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2005-01-06
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Elsevier Science BV
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Abstract
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.
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©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
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Física-Modelos matemáticos, Física matemática
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