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 computation of the monomer density is achieved by solving a consistency equation 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.

A mean-field monomer-dimer model with attractive interaction. Exact solution and rigorous results / Diego Alberici; Pierluigi Contucci; Emanuele Mingione. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 55:(2014), pp. 063301.1-063301.27. [10.1063/1.4881725]

A mean-field monomer-dimer model with attractive interaction. Exact solution and rigorous results

ALBERICI, DIEGO;CONTUCCI, PIERLUIGI;MINGIONE, EMANUELE
2014

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 computation of the monomer density is achieved by solving a consistency equation 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.
2014
A mean-field monomer-dimer model with attractive interaction. Exact solution and rigorous results / Diego Alberici; Pierluigi Contucci; Emanuele Mingione. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 55:(2014), pp. 063301.1-063301.27. [10.1063/1.4881725]
Diego Alberici; Pierluigi Contucci; Emanuele Mingione
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/392743
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