Related papers: Dimer geometry, amoebae and a vortex dimer model

This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of nonzero constant vorticity. A goal is to describe the effects of uniform shear flow on the modulation of weakly nonlinear…

This paper offers a systematic study of a family of graphs called amoebas. Amoebas recently emerged from the study of forced patterns in $2$-colorings of the edges of the complete graph in the context of Ramsey-Turan theory and played an…

We present a general approach for the study of dimer model limit shape problems via variational and integrable systems techniques. In particular we deduce the limit shape of the Aztec diamond and the hexagon for quasi-periodic weights…

We study a supersymmetric partition function of topological vortices in 3d N=4,3 gauge theories on R^2 x S^1, and use it to explore Seiberg-like dualities with Fayet-Iliopoulos deformations. We provide a detailed support of these dualities…

A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…

In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by…

This note relates topics in statistical mechanics, graph theory and combinatorics, lattice quantum field theory, super quantum mechanics and string theory. We give a precise relation between the dimer model on a graph embedded on a torus…

Realizing stable two-dimensional (2D) Dirac points against spin-orbit coupling (SOC) has attracted much attention because it provides a platform to study the unique transport properties. In previous work, Young and Kane [Phys. Rev. Lett.…

The dimer model is the study of random dimer covers (perfect matchings) of a graph. A double-dimer configuration on a graph $G$ is a union of two dimer covers of $G$. We introduce quaternion weights in the dimer model and show how they can…

We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of the moduli spaces (which are symmetric…

We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli…

Inspired by asymptotically flat manifolds, we introduce the concept of asymptotically flat graphs and define the discrete ADM mass on them. We formulate the discrete positive mass conjecture based on the scalar curvature in the sense of…

We study the dimer and Ising models on a finite planar weighted graph with periodic-antiperiodic boundary conditions, i.e. a graph $\Gamma$ in the Klein bottle $K$. Let $\Gamma_{mn}$ denote the graph obtained by pasting $m$ rows and $n$…

Given a weighted graph $G$ embedded in a non-orientable surface $\Sigma$, one can consider the corresponding weighted graph $\widetilde{G}$ embedded in the so-called orientation cover $\widetilde\Sigma$ of $\Sigma$. We prove identities…

The interplay between algebro-geometric and combinatorial Brill-Noether theory is studied. The Brill-Noether variety of a graph shown to be non-empty if the Brill-Noether number is non-negative, as a consequence of the analogous fact for…

To any algebraic curve A in a complex 2-torus $(\C^*)^2$ one may associate a closed infinite region in a real plane called the amoeba of A. The amoebas of different curves of the same degree come in different shapes and sizes. All amoebas…

In this work, we investigate compact K\"ahler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional curvature, which covers various notions of curvature…

We construct Calabi-Yau geometries with wrapped D6 branes which realize ${\cal N}=1$ supersymmetric $A_r$ quiver theories, and study the corresponding geometric transitions. This also yields new large $N$ dualities for topological strings…

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $L(G)$ be the line graph of $G$, which has vertex set $E(G)$ and two vertices $e$ and $f$ of $L(G)$ is adjacent if $e$ and $f$ is incident in $G$. The vertex-edge graph…

We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low energy description corresponds to a quantum dimer model on a dual lattice of even…