skip to main content

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

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.
Authors:
; ;  [1]
  1. Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, Bologna 40126 (Italy)
Publication Date:
OSTI Identifier:
22306253
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; DENSITY; DIMERS; EXACT SOLUTIONS; INTERACTIONS; MEAN-FIELD THEORY; MONOMERS; PHASE SPACE; POTENTIALS