  We have generalized the application of cumulant expansion to ferrimagnetic
systems of large spins. We have derived the effective Hamiltonian in terms of
classical variables for a quantum ferrimagnet of large spins. A noninteracting
gas of ferrimagnetic molecules is studied systematically by cumulant expansion
to second order of ($Js/T$) where $J$ is the exchange coupling in each
molecule, $s$ is the smaller spin ($S_1, s_2$) and $T$ is temperature. We have
observed fairly good results in the convergent regime of the expansion, i.e $T
> Js$. We then extend our approach to a system of interacting ferrimagnetic
molecules. For one dimensional nearest neighbor interaction we have observed
that the correlation of more than two neighboring sites is negligible at
moderate and high temperature behavior. Thus the results of a single molecule
can be applied to the chain of interacting molecules for temperatures greater
than classical energy scale, i.e $T>JS_1s_2$. Finally we will discuss the
effect of spin inhomogeneity on the accuracy of this method.
