21 citations · 55 across the 14 of their papers we have counts for
17 papers
Conformal invariance of the planar four-state Potts model and its random-cluster representation
Emile Averous, Hugo Duminil-Copin, Tiancheng He +2
For the critical random-cluster model on with cluster-weight , we prove the convergence of loops to CLE(4) in the scaling limit. Conformal invariance of the four…
Conformal invariance of the six-vertex model's height function
Emile Averous, Hugo Duminil-Copin, Tiancheng He +2
In this paper, we show that the height function of the six-vertex model in simply connected domains with piecewise constant boundary conditions converges to the Gaussian Free Field…
The BKT transition and surface tension differentiability
Thibault Durand, Piet Lammers
Under the duality between the two-dimensional XY model and an integer-valued height function, the BKT transition is expected to correspond to the disappearance of a corner in the s…
Free energy analyticity of the disordered XY model and Debye screening in the 2D Coulomb gas
Lucas D'Alimonte, Piet Lammers
We consider three models of statistical mechanics: the classical XY model in arbitrary dimension, the lattice Coulomb gas in dimension two, and the square well model in arbitrary d…
Gaussian free field convergence of the six-vertex model with
Hugo Duminil-Copin, Karol Kajetan Kozlowski, Piet Lammers +1
We study the isotropic six-vertex model on with spectral parameter , that is, with weights and .…
Delocalisation and continuity in 2D: loop O(2), six-vertex, and random-cluster models
Alexander Glazman, Piet Lammers
We prove the existence of macroscopic loops in the loop O(2) model with or, equivalently, delocalisation of the associated integer-valued Lipschitz function…
Bijecting the BKT transition
Piet Lammers
We consider the classical XY model (or classical rotor model) on the two-dimensional square lattice graph as well as its dual model, which is a model of height functions. The XY mo…
A dichotomy theory for the height functions of the BKT transition
Piet Lammers
This text considers the discrete height functions associated with the Berezinskii--Kosterlitz--Thouless transition (BKT) at slope zero. Our main results are as follows. * Sharpness…
Non-reversible stationary states for majority voter and Ising dynamics on trees
Piet Lammers, Fabio Toninelli
We study three Markov processes on infinite, unrooted, regular trees: the stochastic Ising model (also known as the Glauber heat bath dynamics of the Ising model), a majority voter…
Height function localisation on trees
Piet Lammers, Fabio Toninelli
We study two models of discrete height functions, that is, models of random integer-valued functions on the vertices of a tree. First, we consider the random homomorphism model, in…
Delocalisation and absolute-value-FKG in the solid-on-solid model
Piet Lammers, Sébastien Ott
The solid-on-solid model is a model of height functions, introduced to study the interface separating the and phase in the Ising model. The planar solid-on-solid model thus…
Height function delocalisation on cubic planar graphs
Piet Lammers
The interest is in models of integer-valued height functions on shift-invariant planar graphs whose maximum degree is three. We prove delocalisation for models induced by convex ne…
Macroscopic behavior of Lipschitz random surfaces
Piet Lammers, Martin Tassy
The motivation for this article is to derive strict convexity of the surface tension for Lipschitz random surfaces, that is, for models of random Lipschitz functions from $\mathbb…
Variational principle for weakly dependent random fields
Piet Lammers, Martin Tassy
Using an alternative notion of entropy introduced by Datta, the max-entropy, we present a new simplified framework to study the minimizers of the specific free energy for random fi…
A generalisation of the honeycomb dimer model to higher dimensions
Piet Lammers
Linde, Moore, and Nordahl introduced a generalisation of the honeycomb dimer model to higher dimensions. The purpose of this article is to describe a number of structural propertie…
The bunkbed conjecture on the complete graph
Peter van Hintum, Piet Lammers
The bunkbed conjecture was first posed by Kasteleyn. If is a finite graph and some subset of , then the bunkbed of the pair is the graph p…
Diffusivity of a walk on fractures of a hypertorus
Piet Lammers
This article studies discrete height functions on the discrete hypertorus. These are functions on the vertices of this hypertorus graph for which the derivative satisfies a specifi…