An evolution equation for the expectation values of the Boltzmann fact
or between monomervalence-bond states is derived. It contains the whol
e information on the thermodynamical and magnetic properties of the sp
in-1/2 quantum Heisenberg model. A new approximation scheme is propose
d and studied in the thermodynamical limit. To lowest order, it leads
to explicit formulas of the internal energy for the antiferromagnetic
Heisenberg model in d dimensions.