  We explicitly calculate the moments t_n of general Heisenberg Hamiltonians up
to sixth order. They have the form of finite sums of products of two factors,
the first factor being represented by a multigraph and the second factor being
a polynomial in the variable s(s + 1), where s denotes the individual spin
quantum number. As an application we determine the corresponding coefficients
of the expansion of the free energy and the zero field susceptibility in powers
of the inverse temperature. These coefficients can be written in a form which
makes explicit their extensive character.
