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

A numerical transfer-matrix approach and diagonalization technique exploiting the point-group symmetry are worked out in the framework of quantum statistical mechanics and group theory as exact simulation tools for application to thermodynamical properties of finite rings. They are applied to the isotropic spin models of the high-nuclearity cyclic clusters [Mn(hfac)2NITPh]6 and Ni12(O2CMe)12(chp)12(H2O)6(THF)6. The microscopic parameters of both molecules (J/kB = 350?10?K and J/kB = 8.5?0.5?K, respectively, with g = 2.23?0.01) are then obtained from a fit of the theoretical susceptibility curves to the experimental results.