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We derive the exact spectra as well as partition functions for a class of$BC_N$ type of spin Calogero models, whose Hamiltonians are constructed byusing supersymmetric analogues of polarized spin reversal operators (SAPSRO).The strong coupling limit of these spin Calogero models yields $BC_N$ type ofPolychronakos-Frahm (PF) spin chains with SAPSRO. By applying the freezingtrick, we obtain an exact expression for the partition functions of such PFspin chains. We also derive a formula which expresses the partition function ofany $BC_N$ type of PF spin chain with SAPSRO in terms of partition functions ofseveral $A_K$ type of supersymmetric PF spin chains, where $K\leq N-1$.Subsequently we show that an extended boson-fermion duality relation is obeyedby the partition functions of the $BC_N$ type of PF chains with SAPSRO. Somespectral properties of these spin chains, like level density distribution andnearest neighbour spacing distribution, are also studied.

Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators