A Mean-Field Monomer–Dimer Model with Randomness: Exact Solution and Rigorous Results

• Published in: Journal of statistical physics Vol. 160; no. 6; pp. 1721 - 1732
• Main Authors: Alberici, Diego, Contucci, Pierluigi, Mingione, Emanuele
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2015; Springer
• Subjects: Mathematical and Computational Physics; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Statistical Physics and Dynamical Systems; Theoretical; Self-averaging; Disordered systems; 82B44; Monomer–dimer models; Random monomer activities

Independent random monomer activities are considered on a mean-field monomer–dimer model. Under very general conditions on the randomness the model is shown to have a self-averaging pressure density that obeys an exactly solvable variational principle. The dimer density is exactly computed in the th...