115 citations · 1.2k across the 68 of their papers we have counts for
9 papers · 1 filter
The Bethe ansatz for the six-vertex and XXZ models: an exposition
Hugo Duminil-Copin, Maxime Gagnebin, Matan Harel +2
In this paper, we review a few known facts on the coordinate Bethe ansatz. We present a detailed construction of the Bethe ansatz vector and energy , which satisfy …
Discontinuity of the phase transition for the planar random-cluster and Potts models with
Hugo Duminil-Copin, Maxime Gagnebin, Matan Harel +2
We prove that the -state Potts model and the random-cluster model with cluster weight undergo a discontinuous phase transition on the square lattice. More precisely, we sh…
Higher order corrections for anisotropic bootstrap percolation
Hugo Duminil-Copin, Aernout C. D. van Enter, Tim Hulshof
We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with -neighbourhood and threshold $r = 3…
The box-crossing property for critical two-dimensional oriented percolation
Hugo Duminil-Copin, Vincent Tassion, Augusto Teixeira
We consider critical oriented Bernoulli percolation on the square lattice . We prove a Russo-Seymour-Welsh type result which allows us to derive several new results c…
Brochette percolation
Hugo Duminil-Copin, Marcelo R. Hilario, Gady Kozma +1
We study bond percolation on the square lattice with one-dimensional inhomogeneities. Inhomogeneities are introduced in the following way: A vertical column on the square lattice i…
Minimal growth harmonic functions on lamplighter groups
Itai Benjamini, Hugo Duminil-Copin, Gady Kozma +1
We study the minimal possible growth of harmonic functions on lamplighters. We find that has no sublinear harmonic functions, $(\mathbb{Z}/2)\wr \mat…