abstract

The monomer–trimer model is studied on the fractal \(3\)-simplex lattice. Configurations are enumerated by an exact system of recurrence relations. Asymptotic forms for the number of pure trimer and monomer–trimer configurations of equal weights as well as entropy are found. The asymptotic form in the close-packed limit differs from the one obtained for dimers on the square lattice. By introducing monomer fugacity, configurations are classified according to the number of monomers (or trimers), and the problem is formulated in the grand canonical ensemble. The average number of monomers and entropy are calculated as functions of fugacity. Entropy as a function of trimer fraction coverage shows qualitatively similar behavior to that found on the square lattice.