Study of the adsorption of interacting dimers on square lattices by using a cluster-exact approximation

A theoretical approach, based on exact calculation of the partition function on finite rectangular clusters, is introduced to study the adsorption of interacting homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for m=(k×l) clusters with m varying from 8 to 48. The adsorption process has been monitored by following thermodynamic properties such as coverage versus chemical potential, internal energy and specific heat of the adlayer, etc. The analytical results are compared with those in [Surf. Sci. 411 (1998) 294], which were obtained by using Monte Carlo simulation and finite-size scaling techniques. The theoretical adsorption isotherms and phase diagrams (critical temperature versus coverage) for both attractive and repulsive lateral interactions are in good qualitative agreement with the computational data. This agreement between simulated and theoretical results supports the validity of the cluster-exact approximation proposed in this paper.