Related papers: Correlation of a macroscopic dent in a wedge with …
We consider a triangular gap of side two in a $90^\circ$ angle on the triangular lattice with mixed boundary conditions: a constrained, zig-zag boundary along one side, and a free lattice line boundary along the other. We study the…
In this paper we enumerate the centrally symmetric lozenge tilings of a hexagon with a fern removed from its center. The proof is based on a variant of Kuo's graphical condensation method. An unexpected connection with the total number of…
In this paper we enumerate the centrally symmetric lozenge tilings of a hexagon with a shamrock removed from its center. Our proof is based on a variant of Kuo's graphical condensation method in which only three of the four involved…
Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a…
We consider triangular holes on the hexagonal lattice and we study their interaction when the rest of the lattice is covered by dimers. More precisely, we analyze the joint correlation of these triangular holes in a ``sea'' of dimers. We…
In this pedagogical paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
In earlier work we showed that in the bulk, the correlation of gaps in dimer systems on the hexagonal lattice is governed, in the fine mesh limit, by Coulomb's law for 2D electrostatics. We also proved that the scaling limit of the discrete…
We study the effect of isospin-symmetry breaking in the framework of the extended Linear Sigma Model (eLSM) in vacuum. In this model, several particles mix with each other at tree level, due to the three non-zero scalar condensates…
We study lozenge tilings of a domain with partially free boundary. In particular, we consider a trapezoidal domain (half hexagon), s.t. the horizontal lozenges on the long side can intersect it anywhere to protrude halfway across. We show…
This paper presents a comprehensive and systematic study of the possible connection between thermalization of cubic nonlinear lattices with nearest-neighbor coupling and the structure of the mixing tensor that arises due to the presence of…
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…
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 deal with unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths $a,b+m,c,a+m,b,c+m$, where an equilateral triangle of side length $m$ has been removed from the center. We give closed formulas for the…
In this paper we determine the interaction of diagonal defect clusters in regions of an Aztec rectangle that scale to arbitrary points on its symmetry axis (in earlier work we treated the case when this point was the center of the scaled…
We consider uniformly random lozenge tilings of simply connected polygons subject to a technical assumption on their limit shape. We show that the edge statistics around any point on the arctic boundary, that is not a cusp or tangency…
In materials science, wedge disclinations are defects caused by angular mismatches in the crystallographic lattice. To describe such disclinations, we introduce an atomistic model in planar domains. This model is given by a…
The thermodynamic properties of vector (O(2) and Complex Spherical) models with four-body interactions are analyzed. When defined in dense topologies, these are effective models for the nonlinear interaction of scalar fields in the presence…
If most of the pixels in an $n \times m$ digital image are the same color, must the image contain a large connected component? How densely can a given set of connected components pack in $\mathbb{Z}^2$ without touching? We answer these two…
We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D.S. Rokhsar and S.A. Kivelson, Phys. Rev.…