The statistics of dimers on a lattice
Web"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. WebConsider a planar rectangular m x n lattice, i.e. a lattice whose horizontal and vertical bonds differ in length. Let the lattice be covered entirely by two sorts of dimers: Ns dimers which …
The statistics of dimers on a lattice
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WebThe Statistics of Dimers on a Lattice. P. W. Kasteleyn. Published 1 December 1961. Mathematics. Physica D: Nonlinear Phenomena. The number of ways in which a finite … WebApr 23, 2024 · (b) Dimer-dimer interactions may result in the resonant formation of a singlon and a linear trimer. (c) Homogeneity η (see text) for V = 30 J evaluated in a 13 × 13 triangular lattice with open boundary conditions for a single dimer (pink dotted), a dimer and three singlons (red solid), and four dimers (blue dashed). The insets indicate the ...
WebMonte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, u BB = u AB =−1, … WebFeb 29, 1988 · The idea of studying the statistics of dimers distributed on square lattices composed of a finite number, M, of infinite strips of equally spaced lattice sites is well known [1]. Various techniques have been developed to study the distribution of fully covered [2] (close packed) lattices, as well as partially covered lattices [3] (refs.
WebThe 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 …
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). hsc do i need to keep my child off schoolWebApr 2, 2024 · This lattice is a bipartite square lattice (Fig. 3c,d) and the ground state moment configuration of the Shakti artificial spin ice is equivalent to a ‘complete cover’, a dimer state for which ... hsc cyclingWebis the problem of dimer statistics [1]. The problem asks for a combinatorial solution to the number of ways of placing k dimers (dumbells) on a lattice containing N points, such that any two dimers are placed in a disjoint manner (i.e., two dimers do not have a common vertex in the lattice). hsce14fsWebAbstract. 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” … hobby lobby in west bend wiWebFor 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 … hobby lobby in waWebDimer 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 ... hobby lobby in webster nyWebDec 15, 1961 · The number of ways of filling the lattice with dimers is calculated exactly for m = n = 8 and is given asymptotically by [exp (2 G π)] 1 2 mn = (1.791 6 2 3) 1 2 mn. The … hobby lobby in wenatchee wa