Probability of Dimer Formation on a Honeycomb Lattice

Atoms adsorbed on a honeycomb lattice diffuse and eventually form dimers. Three types of dimers are possible with this lattice's symmetry: ortho-, meta- and para-dimer. We estimate the probability of para- and ortho-dimer formation when atoms jump independently between sites of the underlying lattice. Our analyze is based on a simple model of diffusive motion of a pair of atoms which bind to lattice sites separated by a distance Delta, measured as a number of edges between sites and characterized by a chirality coefficient chi. Because of diffusive motion of atoms, Delta and chi change in time and we trace a flow over the configurational space. The flow eventually converges to one of possible absorbing states. If the particular adsorbing state is reached it means that a dimer corresponding to this state is formed. We have computed time-dependent probabilities Po and Pp for ortho- and para-dimer formation, respectively. We have found that 4/15 < Po/Pp < 5/14.