  We derive a variational cluster approximation for Heisenberg spin systems at
finite temperature based on the ideas of the self-energy functional theory by
Potthoff for fermionic and bosonic systems with local interactions.
Partitioning the real system into a set of clusters, we find an analytical
expression for the auxiliary free energy, depending on a set of variational
parameters defined on the cluster, whose stationary points provide approximate
solutions from which the thermodynamics of spin models can be obtained. We
explicitly describe the technical details of how to evaluate the free energy
for finite clusters and remark on specific problems and possible limitations of
the method. To test the approximation we apply it to the antiferromagnetic spin
1/2 chain and compare the results for varying cluster sizes and choices of
variational parameters with the exact Bethe ansatz solution.
