Volume-Dependent Cluster Sums and Phase Transition of the Two-Dimensional Triangular Lattice Gas

Abstract

The exact expressions for the volume-dependent cluster sums b l with l ≦5, as functions of λ and T (\(\;=\;\)temperature), are obtained for the two-dimensional triangular lattice gas (with nearest-neighbour interaction) of triangular shape with number of lattice sites (or volume) λ(λ+1)/2. The behaviour of the b l for the case of attractive interaction is studied, and on the basis of the results, the phase transition (condensation) of this lattice gas is discussed by employing Ikeda's theory of condensation of systems with volume-dependent cluster integrals.