Monte Carlo simulations of a two-dimensional hard dimer system

Monte Carlo simulations of a system of two-dimensional hard, homonuclear dimers are reported. The equation-of-state, structural and orientational properties, and the free energy were computed for the fluid phase and several crystalline and non-crystalline (non-periodic) solid structures. The differences in the Gibbs free energy between the various solid structures were found not to exceed 0.1kBT per particle. This is much less than the contribution to the entropy per particle due to degeneracy of the ‘ground state’ of the non-periodic solid which amounts to 0.857kBT. Hence, the thermodynamically stable solid structure of the system corresponds to a set of non-periodic arrangements of the molecular centres of mass and orientations. The coexistence pressure of the non-periodic solid and fluid is determined; it is located within the observed narrow hysteresis region. It is shown that structures of the crystalline solids are well approximated by a simple lattice model.