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Partially solvable spin chains and QES spin models. (English) Zbl 1362.82008

Summary: 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 [A. Enciso et al., J. Phys. A, Math. Theor. 40, No. 8, 1857–1883 (2007; Zbl 1113.81033); Nucl. Phys., B 789, No. 3, 452–482 (2008; Zbl 1151.82318)]. Our discussion focuses on the existence of integer eigenvalues.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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