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A mean-field monomer-dimer model which includes an attractive interactionamong both monomers and dimers is introduced and its exact solution rigorouslyderived. The Heilmann-Lieb method for the pure hard-core interacting case isused to compute upper and lower bounds for the pressure. The bounds are shownto coincide in the thermodynamic limit for a suitable choice of the monomerdensity m. The consistency equation characterising m is studied in the phasespace (h, J), where h tunes the monomer potential and J the attractivepotential. The critical point and exponents are computed and show that themodel is in the mean-field ferromagnetic universality class.

A mean-field monomer-dimer model with attractive interaction. The exact solution