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.

20 pages

References in corpus (3)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• A mean-field monomer-dimer model with random monomer activities. Exact solution and rigorous results
• The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

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