  Effective Hamiltonians are usually constructed by using canonical
transformations or projection techniques. In contrast to this, we present a
method for systems with arbitrary Hilbert space based on the introduction of
cumulants. Cumulants guarantee size consistency, a property that is not always
evident in other treatments. As a nontrivial example of use the derived method
is applied to the strong-coupling limit of the half-filled Hubbard model on a
general lattice in arbitrary spatial dimension for which the fourth-order
expansion in t/U of the effective Hamiltonian is derived.
