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

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...

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Bibliographic Details
Published inJournal of statistical physics Vol. 160; no. 6; pp. 1721 - 1732
Main Authors Alberici, Diego, Contucci, Pierluigi, Mingione, Emanuele
Format Journal Article
LanguageEnglish
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
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Summary: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 thermodynamic limit and shown to be a smooth function.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-015-1306-x