Cluster variation theory of the condensation of atoms in a honeycomb lattice gas with first nearest neighbor exclusion

The condensation of atoms in the honeycomb lattice gas is studied by the cluster variation method. It is assumed that atoms exclude each other from the first nearest neighbor sites and attract each other at farther neighbor sites. When the two (1×1) sublattices have the same potential energy for atoms, the condensation is characterized by the order–disorder phase transition of the first order. Also the second order phase transition takes place at hypercritical temperatures to give rise to a tricritical point. The effect of the third nearest neighbor interaction on the transition behavior is investigated in detail. When the two sublattices give different potential energies to atoms, the second order phase transition is deteriorated to a continuous phase transition between the poorly ordered and the highly ordered phase. The critical temperature as well as the density of the low-density phase for the two-dimensional condensation are found to be higher than those estimated by using a conventional (1×1) triangular lattice gas model.