Journal of Statistical Physics, VoL 35, Nos. 3/4, 1984, p. 285-301.
It is shown that for classical, d-dimensional lattice models with finite-range interactions the translation-invariant equilibrium states have the property that their mean entropy is completely determined by their restriction to a subset of the lattice that is infinite in (d- 1) dimensions and has a width equal to the range of the interaction in the dth dimension. This property is used to show proper convergence toward the exact result for a hierarchy of approximations of the cluster-variation method that uses one-dimensionally increasing basis clusters in a two-dimensional lattice.