Related papers: On loops in the complement to dimers
We consider fermionic fully-packed loop and quantum dimer models which serve as effective low-energy models for strongly correlated fermions on a checkerboard lattice at half and quarter filling, respectively. We identify a large number of…
We perform extensive three-loop tests of the hexagon bootstrap approach for structure constants in planar $\mathcal{N}=4$ SYM theory. We focus on correlators involving two BPS operators and one non-BPS operator in the so-called $SL(2)$…
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…
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities)…
Uniform integer-valued Lipschitz functions on a domain of size $N$ of the triangular lattice are shown to have variations of order $\sqrt{\log N}$. The level lines of such functions form a loop $O(2)$ model on the edges of the hexagonal…
We consider local dynamics of the dimer model (perfect matchings) on hypercubic boxes $[n]^d$. These consist of successively switching the dimers along alternating cycles of prescribed (small) lengths. We study the connectivity properties…
In the dimer model, a configuration consists of a perfect matching of a fixed graph. If the underlying graph is planar and bipartite, such a configuration is associated to a height function. For appropriate "critical" (weighted) graphs,…
We show how decimated Gibbs measures which have an unbroken continuous symmetry due to the Mermin-Wagner theorem, although their discrete equivalents have a phase transition, still can become non-Gibbsian. The mechanism rests on the…
We experimentally study the red-green-blue model, which is a sytem of loops obtained by superimposing three dimer coverings on offset hexagonal lattices. We find that when the boundary conditions are ``flat'', the red-green-blue loops are…
We study the mechanism of loop condensation in the quantum dimer model on the triangular lattice. The triangular lattice quantum dimer model displays a topologically ordered quantum liquid phase in addition to conventionally ordered phases…
We establish a finite-dimensional version of the Arveson-Stinespring dilation theorem for unital completely positive maps on operator systems. This result can be seen as a general principle to deduce finite-dimensional dilation theorems…
We propose a duality between quiver gauge theories and the combinatorics of dimer models. The connection is via toric diagrams together with multiplicities associated to points in the diagram (which count multiplicities of fields in the…
This work continues the study started in \cite{Povolotsky2021}, where the exact densities of loops in the O(1) dense loop model on an infinite strip of the square lattice with periodic boundary conditions were obtained. These densities are…
We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar or embedded on the torus. The set of positive face weights…
The monopole-dimer model introduced recently is an exactly-solvable signed generalisation of the dimer model. We show that the partition function of the monopole-dimer model on a graph invariant under a fixed-point free involution is a…
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 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 show that elements of control theory, together with an application of Harris' ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of networks of…
We consider tiles (dimers) each of which covers two vertices of a rectangular lattice. There is a normalized translation invariant weighting on the shape of the tiles. We study the pressure, p, or entropy, (one over the volume times the…
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…