Solvable scalar and spin models with near-neighbors interactions

Details Solvable scalar and spin models with near-neighbors interactions Solvable scalar and spin models with near-neighbors interactions

2004-07-30

arxiv.org/abs/hep-th/0407274v2

Phys.Lett. B605 (2005) 214-222

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX. Minor typos corrected

Scientific paper

10.1016/j.physletb.2004.11.031

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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