相关论文: A note on dimer models and McKay quivers
In this exposition, we consider the dimer problem on an infinite square lattice with partially non-periodic edge weights, which we refer to as the square lattice with interface. In particular, we compute an exact integral form of the…
We study solvable lattice models associated to canonical Grothendieck polynomials and their duals. We derive inversion relations and Cauchy identities.
We begin a systematic investigation of quench dynamics in higher-dimensional lattice systems considering the case of non-interacting fermions with conserved particle number. We prepare the system in a translational-invariant non-equilibrium…
We introduce the notion of a polyptych lattice, which encodes a collection of lattices related by piecewise linear bijections. We initiate a study of the new theory of convex geometry and polytopes associated to polyptych lattices. In…
We review models of random geometries based on the dynamical lattice approach. We discuss one dimensional model of simplicial complexes (branched polymers), two dimensional model of dynamical triangulations and four dimensional model of…
We present examples of Lax-integrable multi-dimensional systems of partial differential equations with higher local symmetries. We also consider Lagrangian deformations of these equations and construct variational bivectors on them.
Recent work by Forsg{\aa}rd indicates that not every convex lattice polygon arises as the characteristic polygon of an affine dimer or, equivalently, an admissible oriented line arrangement on the torus in general position. We begin the…
We express the finite 3D Dimer partition function as a linear combination of determinants of oriented adjacency matrices, and the finite 3D Ising partition sum as a linear combination of products over aperiodic closed walks. The methodology…
We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock space, we prove a Cauchy identity for…
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…
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper…
A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to…
We present a geometrical approach for studying dimers. We introduce a connection for dimer problems on bipartite and non-bipartite graphs. In the bipartite case the connection is flat but has non-trivial ${\bf Z}_2$ holonomy round certain…
We map certain highly correlated electron systems on lattices with geometrical frustration in the motion of added particles or holes to the spatial defect-defect correlations of dimer models in different geometries. These models are studied…
We discuss factorization of the hypergeometric-type difference equations on the uniform lattices and show how one can construct a dynamical algebra, which corresponds to each of these equations. Some examples are exhibited, in particular,…
We discuss how to construct limit shapes for the domino tiling model (square lattice dimer model) and $5$-vertex model, in appropriate polygonal domains. Our methods are based on the harmonic extension method of [R. Kenyon and I. Prause,…
We show that integrable involutive maps, due to the fact they admit three integrals in separated form, can give rise to equations, which are consistent around the cube and which are not in the multiaffine form assumed in papers [1, 2].…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
Results on semileptonic decay matrix elements of heavy-light mesons and charmonium spectrum and decay constant using a fine quenched lattice are presented.
A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated…