Abstract
The exact expressions for the volume-dependent irreducible cluster sums β k with k ≦7 for the one-dimensional, the two-dimensional square and the three-dimensional simple cubic lattice gas and with k ≦ 4 for the two-dimensional triangular lattice gas, with nearest-neighbour interactions, are obtained. Graphs expressing the volume dependence of β k /β k (0) in the case of attractive interaction are described, where β k (0) is the limit of β k for infinite volume. By the use of these results, the phase transition (condensation) of the lattice gases are discussed.
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