The statistics of dimers on a lattice
WebIn this paper, we present a solution to the close-packed dimer problem on a fractal lattice. The dimer model is canonical model in statistical physics related with many physical phenomena. Originally, it was introduced as a model for adsorption of diatomic molecules on surfaces. Here we assume that the two dimensional substrate on which the adsorption … WebMar 13, 2003 · We consider close-packed dimers, or perfect matchings, on two-dimensional regular lattices. We review known results and derive new expressions for the free energy, …
The statistics of dimers on a lattice
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WebAbstract. The number of ways in which a finite quadratic lattice (with edges or with periodic boundary conditions) can be fully covered with given numbers of “horizontal” and “vertical” … WebJ. M. Hammersley, Calculation of lattice statistics, inProceedings of the Computational Physics Conference (Institute of Physics and the Physical Society, London, 1970), pp. 1–8. ... P. W. Kasteleyn, The statistics of dimers on a lattice I. The number of dimer arrangements on a quadratic lattice.Physica 27:1209–1225 (1961).
WebMar 15, 2001 · The dimer problem on the covering lattice of the plane square lattice is shown to be isomorphic with an eight vertex model, and can be solved exactly when conjugate dimer activities are equal. WebJun 15, 2016 · We study the model of close-packed dimers on planar lattices belonging to the family of modified rectangular (MR) fractals, whose members are enumerated by an integer p ≥ 2, as well as on the non-planar 4-simplex fractal lattice.By applying an exact recurrence enumeration method, we determine the asymptotic forms for numbers of …
WebFor lattices infinite in one or two dimensions asymptotic expressions for this number of dimer configurations are derived, and as an application the entropy of a mixture of dimers … Webto polymers, using the same machinery. The lattice theory of polymer solutions is known as Flory-Huggins theory. In many ways, you will find this theory similar to the small-solute case, except that the statistics are a little more complicated given that a polymer is a connected entity. Figure 1 shows a lattice model of a polymer.
WebDimer Statistics and Phase Transitions. After the introduction of the concept of lattice graph and a brief discussion of its role in the theory of the Ising model, a related combinatorial problem is discussed, namely that of the statistics of non-overlapping dimers, each occupying two neighboring sites of a lattice graph. It is shown that the ...
WebInternational Nuclear Information System (INIS) IAEA flower shops in ionia michiganWebJul 11, 2024 · Lattice dimer statistics in two-dimension gained momentum in 1961 when the exact solution of the enumeration of pure dimer coverings of a rectangular square lattice was found by Kasteleyn (Physica 27:1209–1225) and Temperley and Fisher (Philos Magn 6:1061–1063). Recently the author introduced the state matrix recursion method to … flower shops in iota laWebDec 22, 2004 · After the introduction of the concept of lattice graph and a brief discussion of its role in the theory of the Ising model, a related combinatorial problem is discussed, … flower shops in iowa city iaWebThe first studies of the statistics of dimer coverings of a lattice were carried out more than 50 years ago,6–8 obtaining results analogous to those of the Bethe approximation9–11 … flower shops in inverurie in aberdeenshireWeb"vertical" dimers is rigorously calculated by a combinatorial method involving Pfaffians. For lattices infinite in one or two dimensions asymptotic expressions for this number of dimer configurations are derived, and as an application the entropy of a mixture of dimers of two different lengths on an infinite rectangular lattice is calculated. flower shops in indioWebThe number of ways in which a finite quadratic lattice (with edges or with periodic boundary conditions) can be fully covered with given numbers of “horizontal” and “vertical” dimers is … flower shops in iowa park txWebFeb 1, 2016 · The statistics of dimers on a lattice. Physica (1961) M.E. Fisher Statistical mechanics of dimers on a plane lattice. Phys. Rev. (1961) P.W. Kasteleyn Dimer statistics and phase transition. J. Math. Phys. (1963) P.W. Kasteleyn Graph theory and crystal physics; H.N.V. Temperley et al. Dimer problem in statistical mechanics—an exact result. flower shops in inwood wv