Exact Result for the Thermal Average of theS=12Isotropic Heisenberg Hamiltonian

An exact expression for the thermal average of the $S=\frac{1}{2}$ isotropic Heisenberg Hamiltonian has been derived which, in contrast to an exact result derived by Mills, is identical in form to a well-known result for boson systems with two-body interactions. A generalization of the result is found to be correct for $S>\mathrm{}\frac{1}{2}$ at low temperatures. It is shown that correct low-temperature results can be obtained from a wide range of approximate magnon spectra. This constitutes a major advantage over the result derived by Mills.