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The monomer-dimer problem is studied for several two- and three-dimensional lattices (coordination number q by deriving between 8 and 16 coefficients of the exact series expansions in powers of the activity z and density ρ of dimers.
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Dimers can be placed on the edges of G so that no vertex has more than one dimer. Uncovered vertices are called monomers and have a fugacity which we call x.
Oct 1, 2010 · In this paper we derive the solution by mapping the problem onto one on close-packed dimers on a related lattice. Finite-size analysis of the ...
The problem of monomer–dimer statistics is not only mathematically intriguing but has a large variety of applications in physics and chemistry. It is important ...
Jan 12, 1996 · A classical technique due to Fisher, Kasteleyn and Temperley solves the problem exactly in two dimensions when the number of monomers is zero ( ...
Counting monomer-dimers, or equivalently, matchings of a graph G, is an interesting but intriguing question with great difficulties in statistical physics.
We investigate the general monomer-dimer partition function,P(x), which is a polynomial in the monomer activity,x, with coefficients depending on the dimer.
Jan 23, 2019 · This method proceeds with a recurrence relation of so-called state matrices of large size. The enumeration problem of pure dimer coverings and ...
This paper extends, to the more general case of the multidimensional monomer-dimer problem, some earlier work (Hammersley, 1968) on the dimer problem.
Statement of the problem and principal results. Denote by A(n, d) the set of sites of the d-dimensional hypercubical lattice having integer coordinates.