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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.
Abstract. We investigate the general monomer-dimer partition function, P(x), which is a polynomial in the monomer activity, x, with coefficients depending ...
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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 ( ...
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 ...
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.
Horizontal and vertical dimers are considered as x -dimers and y -dimers, respectively. Dimers must be placed so that no vertex belongs to more than one dimer.
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 ...
methods to formulate and solve this problem. Various methods have been used to study the monomer-dimer problem, and to estimate tIt) for three-dimensional.
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.