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

Journal Article · Sun Jun 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4881725· OSTI ID:22306253

Alberici, D., E-mail: [e-mail]; Contucci, P., E-mail: [e-mail]; Mingione, E., E-mail: [e-mail] ^[1]

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1. Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, Bologna 40126 (Italy)

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.

• OSTI ID: 22306253
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPUTERIZED SIMULATION
DENSITY
DIMERS
EXACT SOLUTIONS
INTERACTIONS
MEAN-FIELD THEORY
MONOMERS
PHASE SPACE
POTENTIALS