Monomer-Dimer Mixture on a Honeycomb Lattice

We study a monomer-dimer mixture defined on a honeycomb lattice as a toy model for the spin ice system in a magnetic field. In a low-doping region of monomers, the effective description of this system is given by the dual sine-Gordon model. In intermediate- and strong-doping regions, the Potts lattice gas theory can be employed. Synthesizing these results, we construct a renormalization-group flow diagram, which includes the stable and unstable fixed points corresponding to ${\mathcal{M}}_5$ and ${\mathcal{M}}_6$ in the minimal models of the conformal field theory. We perform numerical transfer-matrix calculations to determine a global phase diagram and also to proffer evidence to check our prediction.