The statistics of dimers on a lattice
WebSep 1, 1989 · An important, even though physically oversimplified model of a system (e.g. solution or gas) containing diatomic molecules is that of a lattice occupied by ‘rigid dimers’ (e.g. Fowler and ... 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.
The statistics of dimers on a lattice
Did you know?
WebInternational Nuclear Information System (INIS) IAEA 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” …
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 … WebSep 15, 2024 · 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 …
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 ... 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 …
WebJul 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 …
WebJun 15, 2011 · Kasteleyn had derived explicit expressions of the number of perfect matchings for Qm,n,0 (P.W. Kasteleyn, The statistics of dimers on a lattice I: The number of dimer arrangements on a quadratic ... kuvert gamla maifWebMonte 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, … kuvika badestrandWebJun 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 … jay neukom debevoiseWebDec 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 … jay neukom skaddenWebWe discuss the exact solutions of various models of the statistics of dimer coverings of a Bethe lattice. We reproduce the well-known exact result for noninteracting hard-core … kuvet terbuat dariWebThe 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 … kuvh sandalsWebDec 1, 2006 · Surprisingly the partition function for "maximal coverage" on the Bethe lattice is identical to that for the statistics of branched polymers when the activity for a … kuvings canada