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math-ph2013★ 18 cited
A mean-field monomer-dimer model with attractive interaction. The exact solution
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb…
math-ph2013★ 17 cited
Solution of the monomer-dimer model on locally tree-like graphs. Rigorous results
Diego Alberici, Pierluigi Contucci
We consider the monomer-dimer model on sequences of random graphs locally convergent to trees. We prove that the monomer density converges almost surely, in the thermodynamic limit…