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Abstract
In this paper we prove an extension of the usual freezing trick argument which can be applied to a number of quasi-exactly solvable spin models of Calogero–Sutherland type. In order to illustrate the application of this method we analyze a partially solvable spin chain presenting near-neighbors interactions which was introduced and studied in J. Phys. A: Math. Theor. 40 (2007) 1857–1883; Nucl. Phys. 789 (2008) 452–482. Our discussion focuses on the existence of integer eigenvalues.