A mean-field monomer-dimer model with random monomer activities. Exact solution and rigorous results

Abstract

Independent random monomer activities are considered on a mean-feld monomer-dimer model. Under very general conditions on the randomness the model is shown to have a self-averaging pressure density that obeys a solvable variational principle. The dimer density is exactly computed in the thermodynamic limit and shown to be a smooth function.Comment: 20 page