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Related papers: Height fluctuations in non-integrable classical di…

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We consider a non-integrable model for interacting dimers on the two-dimensional square lattice. Configurations are perfect matchings of $\mathbb Z^2$, i.e. subsets of edges such that each vertex is covered exactly once ("close-packing"…

Probability · Mathematics 2017-02-13 Alessandro Giuliani , Vieri Mastropietro , Fabio Lucio Toninelli

We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer…

Mathematical Physics · Physics 2020-07-14 Alessandro Giuliani , Vieri Mastropietro , Fabio Lucio Toninelli

In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including:…

Probability · Mathematics 2019-10-23 Alessandro Giuliani , Fabio Lucio Toninelli

In this paper we investigate the height field of a dimer model/random domino tiling on the plane at a smooth-rough (i.e. gas-liquid) transition. We prove that the height field at this transition has two-point correlation functions which…

Mathematical Physics · Physics 2023-01-31 Scott Mason

We consider a model of weakly interacting, close-packed, dimers on the two-dimensional square lattice. In a previous paper, we computed both the multipoint dimer correlations, which display non-trivial critical exponents, continuously…

Statistical Mechanics · Physics 2017-04-05 Alessandro Giuliani , Vieri Mastropietro , Fabio Lucio Toninelli

The dimer model on a planar bipartite graph can be viewed as a random surface measure. We study these fluctuations for a dimer model on the square grid with two different classes of weights and provide a condition for their equivalence. In…

Probability · Mathematics 2015-05-27 Sunil Chhita

We study perfect matchings on the square-hexagon lattice with $1\times n$ periodic edge weights such that the boundary condition is given by either (1) each remaining vertex on the bottom boundary is followed by $(m-1)$ removed vertices;…

Probability · Mathematics 2018-09-25 Zhongyang Li

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,…

Probability · Mathematics 2014-07-24 Julien Dubédat

The purpose of this note is to give a succinct summary of some basic properties of T-graphs which arise in the study of the dimer model. We focus in particular on the relation between the dimer model on the heaxgonal lattice with a given…

Probability · Mathematics 2016-10-26 Nathanaël Berestycki , Benoit Laslier , Gourab Ray

In this paper, we consider the near-critical dimer model in the setup of isoradial superpositions with Temperleyan boundary conditions. We show that the centered height function converges as the mesh size tends to zero to a limiting field…

Probability · Mathematics 2026-03-09 Nathanaël Berestycki , Scott Mason , Lucas Rey

We prove that the truncated correlation functions of the charge and gradient fields associated with the massless sine-Gordon model on $\mathbb{R}^2$ with $\beta=4\pi$ exist for all coupling constants and are equal to those of the chiral…

Mathematical Physics · Physics 2025-08-21 Roland Bauerschmidt , Christian Webb

We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the…

Mathematical Physics · Physics 2014-08-26 Jeffrey Kuan

We analyze height fluctuations in Aztec diamond dimer models with nearly arbitrary periodic edge weights. We show that the centered height function approximates the sum of two independent components: a Gaussian free field on the multiply…

Probability · Mathematics 2025-04-01 Tomas Berggren , Matthew Nicoletti

We derive a field theory for the two-dimensional classical dimer model by applying bosonization to Lieb's (fermionic) transfer-matrix solution. Our constructive approach gives results that are consistent with the well-known height theory,…

Statistical Mechanics · Physics 2023-06-01 Neil Wilkins , Stephen Powell

Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and…

We consider the dimer model in cylindrical domains $\Omega_\delta$ on square grids of mesh size $\delta$ with two Temperleyan boundary components of different colors. Assuming that the $\Omega_\delta$ approximate a cylindrical domain…

Probability · Mathematics 2026-01-21 Dmitry Chelkak , Zachary Deiman

We study a model of random surfaces arising in the dimer model on the honeycomb lattice. For a fixed ``wire frame'' boundary condition, as the lattice spacing $\epsilon\to0$, Cohn, Kenyon and Propp [CKP] showed the almost sure convergence…

Mathematical Physics · Physics 2007-06-13 Richard Kenyon

We analyze asymptotic height function fluctuations in uniformly random domino tiling models on multiply connected Temperleyan domains. Starting from asymptotic formulas derived by Kenyon [arXiv:math-ph/9910002v1], we show that (1) the…

Probability · Mathematics 2025-04-29 Matthew Nicoletti

We study one-point functions of the sine-Gordon model on a cylinder. Our approach is based on a fermionic description of the space of descendent fields, developed in our previous works for conformal field theory and the sine-Gordon model on…

High Energy Physics - Theory · Physics 2013-04-25 M. Jimbo , T. Miwa , F. Smirnov

We study a model of fully-packed dimer configurations (or perfect matchings) on a bipartite periodic graph that is two-dimensional but not planar. The graph is obtained from $\mathbb Z^2$ via the addition of an extensive number of extra…

Probability · Mathematics 2023-12-06 Alessandro Giuliani , Bruno Renzi , Fabio Toninelli
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