Related papers: Classical Dimers on Penrose Tilings
In the present paper, we investigate the maximal degree of minimal generators of the toric ideal of the matching polytope of a graph. It is known that the toric ideal associated to a bipartite graph is generated by binomials of degree at…
Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer…
We employ a classical limit grounded in SU(4) coherent states to investigate the temperature-dependent dynamical spin structure factor of the $S = 1/2$ ladder consisting of weakly coupled dimers. By comparing the outcomes of this classical…
We numerically examine the depinning, sliding, and melting of commensurate and incommensurate Wigner crystals on two-dimensional hexagonal periodic substrates near fillings of 1/3, 1/2, and 2/3 to model the dynamics of generalized Wigner…
The theory and design of superbackscattering nanoparticle dimers are presented. We analytically derive the optimal configurations and the upper bound of their backscattering cross-sections. In particular, it is demonstrated that…
This paper is intended to provide an introduction to the theory of substitution tilings. For our purposes, tiling substitution rules are divided into two broad classes: geometric and combinatorial. Geometric substitution tilings include…
The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer coverings in two dimensions. In earlier work, Stanley proved a…
Local and fast structural probes using synchrotron radiation have shown nanoscale striped puddles and nanoscale phase separation in doped perovskites.It is known that the striped phases in doped perovskites are due to competing interactions…
There are two main classes of physics-based models for two-dimensional cellular materials: packings of repulsive disks and the vertex model. These models have several disadvantages. For example, disk interactions are typically a function of…
We show that a symmetric superposition of five standing plane waves can be expressed as an infinite series of terms of decreasing wavenumber, where each term is a product of five plane waves. We show that this series converges pointwise in…
We study a model of colored multiwebs, which generalizes the dimer model to allow each vertex to be adjacent to \(n_v\) edges. These objects can be formulated as a random tiling of a graph with partial dimer covers. We examine the case of a…
This paper describes a recomposition of the rhombic Penrose aperiodic protoset due to Robert Ammann. We show that the three prototiles that result from the recomposition form an aperiodic protoset in their own right without adjacency rules.…
Suppose $k\nmid n$ and $H$ is an $n$-vertex $k$-uniform hypergraph. A near perfect matching in $H$ is a matching of size $\lfloor n/k\rfloor$. We give a divisibility barrier construction that prevents the existence of near perfect matchings…
We consider the dimer model in cylindrical domains $\Omega_\delta$ on square grids of mesh size $\delta$ with two Temperleyan boundary components of different colors. Assuming that the $\Omega_\delta$ approximate a cylindrical domain…
We identify the maximally dense lattice packings of tangent-disk trimers with fixed bond angles ($\theta = \theta_0$) and contrast them to both their nonmaximally-dense-but-strictly-jammed lattice packings as well as the disordered jammed…
Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function…
We construct families of discrete solitons (DSs) in an array of self-defocusing waveguides with an embedded $\mathcal{PT}$ (parity-time)-symmetric dimer, which is represented by a pair of waveguides carrying mutually balanced gain and loss.…
We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong…
Quasiperiodic pinning arrays, as recently demonstrated theoretically and experimentally using a five-fold Penrose tiling, can lead to a significant enhancement of the critical current Ic as compared to "traditional" regular pinning arrays.…
In the past three decades, the study of rhombus tilings and domino tilings of various plane regions has been a thriving subfield of enumerative combinatorics. Physicists classify such work as the study of dimer covers of finite graphs. In…