Order–disorder phase transitions in a honeycomb lattice gas with first nearest neighbor exclusion: comparison between different approximations and a Monte Carlo simulation

The order–disorder phase transitions in a honeycomb lattice gas have been studied in the Bragg–Williams (BW) and the quasi-chemical (QC) approximations as well as by means of Monte Carlo simulations. The model system, which is the same as studied by the cluster variation method (CVM) in a previous paper, contains the first nearest neighbor exclusion and the second nearest neighbor attraction. Simple analytical expressions of thermodynamic functions have been derived in the BW and QC approximations, which will provide a useful tool for semi-quantitative analysis of experimental observations. In every method the lattice gas has been found to undergo both the phase transition of the first order and that of the second order to give rise to the tricritical point. However, the second order transition has been found to be limited to within a finite temperature in the BW approximation, while the other methods including CVM allow the phase transition to occur at infinitely high temperature. The tricritical temperatures calculated by BW and QC are about two times higher than the MC simulations. The previous CVM calculation has been found to give the tricritical temperature only a little lower than in BW and QC. The reason why the previous CVM is not so accurate as expected is discussed on the basis of the network arrangement of clusters at the limit where one of the two (1 × 1)-1/2 triangular sublattices can be neglected.