Transfer matrix simulation of hard-core lattice gases on triangular lattice with up to third-neighbour exclusion

Abstract

The hard-core lattice gas on a triangular lattice with up to thirdneighbour exclusion has been simulated by the transfer matrix
method. To calculate the transfer matrix a special algorithm for generating rings is used. The algorithm is based on the selection of admissible states of rings directly in the process of their construction. This approach allows us to increase the available sizes of rings. Isotherms have been constructed for all three models. For the first and second models, the previously obtained results are reproduced. For the third model, it is found that there is a first-order phase transition and the unit cell size of the ordered phase is equal to seven.