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arXiv · 1311.6551

A mean-field monomer-dimer model with attractive interaction. The exact solution

Diego Alberici·Pierluigi Contucci·Emanuele Mingione
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Abstract

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 method for the pure hard-core interacting case is used to compute upper and lower bounds for the pressure. The bounds are shown to coincide in the thermodynamic limit for a suitable choice of the monomer density m. The consistency equation characterising m is studied in the phase space (h, J), where h tunes the monomer potential and J the attractive potential. The critical point and exponents are computed and show that the model is in the mean-field ferromagnetic universality class.

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Diego Alberici, Pierluigi Contucci, Emanuele Mingione. 2013-11-26. A mean-field monomer-dimer model with attractive interaction. The exact solution. https://doi.org/10.1063/1.4881725

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