Exact simulations of quantum rings and characterization of hexanuclear manganese and dodecanuclear nickel cyclic complexes

A numerical transfer-matrix approach and diagonalization technique exploiti ng the point-group symmetry are worked out in the framework of quantum stat istical mechanics and group theory as exact simulation tools for applicatio n to thermodynamical properties of finite rings. They are applied to the is otropic spin models of the high-nuclearity cyclic clusters [Mn(hfac)(2)NITP h](6) and Ni-12(O2CMe)(12)(Chp)(12)(H2O)(6)(THF)(6). The microscopic parame ters of both molecules (J/k(B) = 350 +/- 10 K and J/k(B) = 8.5 +/- 0.5 K, r espectively, with g = 2.23 +/- 0.01) are then obtained from a fit of the th eoretical susceptibility curves to the experimental results.