  Based on the self-energy-functional approach proposed recently [M. Potthoff,
Eur. Phys. J. B 32, 429 (2003)], we present an extension of the
cluster-perturbation theory to systems with spontaneously broken symmetry. Our
method applies to models with local interactions and accounts for both
short-range correlations and long-range order. Short-range correlations are
accurately taken into account via exact diagonalization of finite clusters.
Long-range order is described by variational optimization of a ficticious
symmetry-breaking field. In comparison with related cluster methods, our
approach is more flexible and, for a given cluster size, less demanding
numerically, especially at zero temperature. An application of the method to
the antiferromagnetic phase of the Hubbard model at half-filling shows good
agreement with results from quantum Monte-Carlo calculations. We demonstrate
that the variational extension of the cluster-perturbation theory is crucial to
reproduce salient features of the single-particle spectrum.
