  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.
