In statistical mechanics, the cluster expansion (also called the high temperature expansion or hopping expansion) is a power series expansion of the partition function of a statistical field theory around a model that is a union of non-interacting 0-dimensional field theories. Unlike the usual perturbation expansion which usually leads to a divergent asymptotic series, the cluster expansion may converge within a non-trivial region, in particular when the interaction is small and short-ranged.
The cluster expansion coefficients are calculated by intricate combinatorial counting. See [1] for a tutorial review.