Related papers: Macroscopically separated gaps in dimer coverings …
The correlation of gaps in dimer systems was introduced in 1963 by Fisher and Stephenson, who looked at the interaction of two monomers generated by the rigid exclusion of dimers on the closely packed square lattice. In previous work we…
The original motivation for this paper goes back to the mid-1990's, when James Propp was interested in natural situations when the number of domino tilings of a region increases if some of its unit squares are deleted. Guided in part by the…
In Bain [J. Math. Phys. 64, 023301 (2023)], we found asymptotics of one-point correlation functions of the two-periodic weighted Aztec diamond in the mesoscopic limit, where the linear size of the ordered region is of the same order as the…
In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby…
The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated Non-Intersecting Lattice Path…
As part of our ongoing work on the enumeration of symmetry classes of lozenge tilings of hexagons with certain four-lobed structures removed from their center, we consider the case of the tilings which are both vertically and horizontally…
We investigate the universal orientation-dependent interactions between non-spherical colloidal particles immersed in a critical solvent by studying the instructive paradigm of a needle embedded in bounded two-dimensional Ising models at…
Three phases of macroscopic domains have been seen for large but finite periodic dimer models; these are known as the frozen, rough and smooth phases. The transition region between the frozen and rough region has received a lot of attention…
We present a detailed study of a model of close-packed dimers on the square lattice with an interaction between nearest-neighbor dimers. The interaction favors parallel alignment of dimers, resulting in a low-temperature crystalline phase.…
The Casimir interaction between one-dimensional metallic objects (cylinders, wires) displays unconventional features. Here we study the orientation dependence of this interaction by computing the Casimir energy between two inclined…
Fairly shortly after the publication of the Aztec diamond theorem of Elkies, Kuperberg, Larsen and Propp in 1992, interest arose in finding the number of domino tilings of an Aztec diamond with an ``Aztec window,'' i.e.\ a hole in the shape…
In this work, we consider the Casimir effect due to massless fermionic fields in the presence of long cylinders. More precisely, we consider the interaction between a cylinder parallel to a plate, between two parallel cylinders outside each…
We discuss the expansion of interaction kernels between anisotropic rigid molecules. The expansion decouples the correlated orientational variables so that it can be utilized to derive macroscopic models. Symmetries of two types are…
The entanglement asymmetry is an information based observable that quantifies the degree of symmetry breaking in a region of an extended quantum system. We investigate this measure in the ground state of one dimensional critical systems…
We calculate the Casimir interaction between two short range scatterers embedded in a background of one dimensional massless Dirac fermions using a force operator approach. We obtain the force between two finite width square barriers, and…
We prove an asymptotic formula for the probability that, if one chooses a domino tiling of a large Aztec diamond at random according to the uniform distribution on such tilings, the tiling will contain a domino covering a given pair of…
We consider asymtotics of a domino tiling model on a class of domains which we call rectangular Aztec diamonds. We prove the Law of Large Numbers for the corresponding height functions and provide explicit formulas for the limit. For a…
A multiple scattering formulation is used to calculate the force, arising from fluctuating scalar fields, between distinct bodies described by $\delta$-function potentials, so-called semitransparent bodies. (In the limit of strong coupling,…
We use a disordered anti-ferromagnetic spin-1/2 chain with anisotropic exchange coupling to model an array of interacting qubits. All qubits have the same level spacing, except two, which are called the defects of the chain. The level…
The interaction of an interfacial crack with small impurities is analysed on the basis of an asymptotic formula derived by the authors. The interaction between the main crack and the defects (e.g. small cracks or inclusions) is described…