相关论文: Dimers on a simple-quartic net with a vacancy

The classical 1961 solution to the problem of determining the number of perfect matchings (or dimer coverings) of a rectangular grid graph -- due independently to Kasteleyn and to Temperley and Fisher -- consists of changing the sign of…

We solve the monomer-dimer problem on a non-bipartite lattice, the simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the non-bipartite nature of the lattice, the well-known…

In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model {\it via}…

The classical monomer-dimer model in two-dimensional lattices has been shown to belong to the \emph{``#P-complete''} class, which indicates the problem is computationally ``intractable''. We use exact computational method to investigate the…

The exact enumeration of pure dimer coverings on the square lattice was obtained by Kasteleyn, Temperley and Fisher in 1961. In this paper, we consider the monomer-dimer covering problem (allowing multiple monomers) which is an outstanding…

Following the recent proposal made by Bouttier et al [Phys. Rev. E 76, 041140 (2007)], we study analytically the mobility properties of a single vacancy in the close-packed dimer model on the square lattice. Using the spanning web…

We present an application of the Grassmann algebra to the problem of the monomer-dimer statistics on a two-dimensional square lattice. The exact partition function, or total number of possible configurations, of a system of dimers with a…

We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble by Pfaffians. This model is particularly interesting for, unlike the dimer problems…

We use computational method to investigate the number of ways to pack dimers on \emph{odd-by-odd} lattices. In this case, there is always a single vacancy in the lattices. We show that the dimer configuration numbers on $(2k+1) \times…

We consider the dimer model on a bipartite graph embedded into a locally flat Riemann surface with conical singularities and satisfying certain geometric conditions in the spirit of the work of [Chelkak, Laslier and Russkikh, Proceedings of…

Covering a graph or a lattice with non-overlapping dimers is a problem that has received considerable interest in areas such as discrete mathematics, statistical physics, chemistry and materials science. Yet, the problem of percolation on…

We consider a non-integrable model for interacting dimers on the two-dimensional square lattice. Configurations are perfect matchings of $\mathbb Z^2$, i.e. subsets of edges such that each vertex is covered exactly once ("close-packing"…

Using classical density functional theory, we study the behavior of dimers, i.e. hard rods of length $L=2$, on a two-dimensional cubic lattice. For deriving a free energy functional, we employ Levy's prescription which is based on the…

We present analytic results for a special dimer model on the {\em non-bipartite} and {\em non-planar} checkerboard lattice that does not allow for parallel dimers surrounding diagonal links. We {\em exactly} calculate the number of closed…

We discuss the exact solutions of various models of the statistics of dimer coverings of a Bethe lattice. We reproduce the well-known exact results for noninteracting hard-core dimers by both a very simple geometrical argument and a general…

The correlation functions of an arbitrary number of boundary monomers in the system of close-packed dimers on the square lattice are computed exactly in the scaling limit. The equivalence of the 2n-point correlation functions with those of…

In a recent paper [ F. Wang and F. Y. Wu, Phys. Rev. E 75 (2007) 040105(R) ] we reported exact results on the enumeration of close-packed dimers on an infinite kagome lattice. We computed the per-dimer free energy using both the Pfaffian…

It is shown that dimers is Yang-Baxter integrable as a six-vertex model at the free-fermion point with crossing parameter $\lambda=\tfrac{\pi}{2}$. A one-to-many mapping of vertex onto dimer configurations allows the free-fermion solutions…

In this exposition, we consider the dimer problem on an infinite square lattice with partially non-periodic edge weights, which we refer to as the square lattice with interface. In particular, we compute an exact integral form of the…

We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency…