Trimer-Monomer Mixture Problem on (111) $1\times 1$ Surface of Diamond Structure

We consider a system of trimers and monomers on the triangular lattice, which describes the adsorption problem on (111) $1\times 1$ surface of diamond structure. We give a mapping to a 3-state vertex model on the square lattice. We treat the problem by the transfer-matrix method combined with the density-matrix algorithm, to obtain thermodynamic quantities.