A mean-field monomer-dimer model with random monomer activities. Exact   solution and rigorous results
  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. 
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
math-ph cond-mat.stat-mech math.MP math.PR