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Related papers: Dimers in piecewise Temperleyan domains

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We rigorously establish the asymptotic equivalence between the height function of interacting dimers on the square lattice and the massless Gaussian free field. Our theorem explains the microscopic origin of the sine-Gordon field theory…

Statistical Mechanics · Physics 2015-06-23 Alessandro Giuliani , Vieri Mastropietro , Fabio Lucio Toninelli

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

We present a comprehensive tensor network study of staggered, Wilson, and twisted mass fermions in the Hamiltonian formulation, using the massive two-flavor Schwinger model as a benchmark. Particular emphasis is placed on twisted mass…

High Energy Physics - Lattice · Physics 2026-04-14 Tim Schwägerl , Karl Jansen , Stefan Kühn

In the limit of the lattice spacing going to zero, we consider the dimer model on isoradial graphs in the presence of singular $SL(N,\mathbb{C})$ gauge fields flat away from a set of punctures. We consider the cluster expansion of this…

High Energy Physics - Theory · Physics 2023-10-26 Sri Tata

We present results of the Monte-Carlo simulations for scaling of the free energy in dimers on the hexagonal lattice. The traditional Markov-chain Metropolis algorithm and more novel non-Markov Wang-Landau algorithm are applied. We compare…

Statistical Mechanics · Physics 2022-01-26 Pavel Belov , Aleksandr Enin , Anton Nazarov

The double-dimer model consists in superimposing two independent, identically distributed perfect matchings on a planar graph, which produces an ensemble of non-intersecting loops. Kenyon established conformal invariance in the small mesh…

Probability · Mathematics 2014-03-25 Julien Dubédat

The dimer model is an exactly solvable model of planar statistical mechanics. In its critical phase, various aspects of its scaling limit are known to be described by the Gaussian free field. For periodic graphs, criticality is an algebraic…

Probability · Mathematics 2015-06-22 Julien Dubédat , Reza Gheissari

We consider the dimer model on the square and hexagonal lattices with doubly periodic weights. The purpose of this paper is threefold: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov (and…

Probability · Mathematics 2024-10-21 Nathanaël Berestycki , Levi Haunschmid-Sibitz

We define a scaling limit of the height function on the domino tiling model (dimer model) on simply-connected regions in Z^2 and show that it is the ``massless free field'', a Gaussian process with independent coefficients when expanded in…

Mathematical Physics · Physics 2007-05-23 R. Kenyon

Given a bounded Riemann surface $M$ of finite topological type, we show the existence of a universal and conformally invariant scaling limit for the Temperleyan cycle-rooted spanning forest on any sequence of graphs which approximate $M$ in…

Probability · Mathematics 2024-12-11 Nathanaël Berestycki , Benoit Laslier , Gourab Ray

The correlation functions of an arbitrary number of boundary monomers in the system of close-packed dimers on the square lattice are computed exactly in the scaling limit. The equivalence of the 2n-point correlation functions with those of…

Statistical Mechanics · Physics 2008-11-26 Vyatcheslav B. Priezzhev , Philippe Ruelle

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

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

We study the universal scaling behavior of the entanglement entropy of critical theories in $2+1$ dimensions. We specially consider two fermionic scale-invariant models, free massless Dirac fermions and a model of fermions with quadratic…

Strongly Correlated Electrons · Physics 2015-02-24 Xiao Chen , Gil Young Cho , Thomas Faulkner , Eduardo Fradkin

We propose a discretisation scheme based on the Dirac-Kahler formalism (DK) in which the algebraic relations between continuum operators ${\wedge, d, \star}$ are captured by their discrete analogues, allowing the construction of the…

High Energy Physics - Theory · Physics 2007-05-23 Vivien de Beauce , Samik Sen

We establish bounds on the decay of time-dependent multipoint correlation functionals of one-dimensional quasi-free fermions in terms of the decay properties of their two-point function. At a technical level, this is done with the help of…

Mathematical Physics · Physics 2016-04-20 Robert Sims , Simone Warzel

In this work we study the variational problem associated to dimer models, a class of models from integrable probability and statistical mechanics in dimension two which have been the focus of intense research efforts over the last decades.…

Analysis of PDEs · Mathematics 2025-12-09 Kari Astala , Erik Duse , István Prause , Xiao Zhong

The spectrum of massless Dirac fermions on the surface of a topological insulator in a perpendicular magnetic field $B$ contains a $B$-independent "zeroth Landau level", protected by chiral symmetry. If the Dirac equation is discretized on…

Mesoscale and Nanoscale Physics · Physics 2023-08-25 A. Donís Vela , G. Lemut , J. Tworzydło , C. W. J. Beenakker

We apply strong-coupling perturbation theory to gauge theories containing domain-wall fermions in Shamir's surface version. We construct the effective Hamiltonian for the color-singlet degrees of freedom that constitute the low-lying…

High Energy Physics - Lattice · Physics 2009-10-31 Richard C. Brower , Benjamin Svetitsky

In this paper, we identify the scaling limit of the fermionic discrete Gaussian free field (fDGFF) as a logarithmic conformal field theory (CFT) in two dimensions. We first establish a one-to-one correspondence between the space of local…

Mathematical Physics · Physics 2025-11-26 David Adame-Carrillo , Wioletta M. Ruszel