10 citations · 10 across the 3 of their papers we have counts for
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Rotational invariance in critical planar lattice models
Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun +2
We prove that the large-scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the squ…
Near-critical Ornstein--Zernike theory for the planar random-cluster model
Lucas D'Alimonte, Ioan Manolescu
We develop an Ornstein--Zernike theory for the two-dimensional random-cluster model with that also applies in its near-critical regime. In particular, we prove an asy…
Critical exponents for planar random-cluster model with cluster-weight
Hong-Bin Chen, Hugo Duminil-Copin, Tiancheng He +4
Using the Baxter-Kelland-Wu coupling and the convergence of the height function of the six-vertex model to the Gaussian Free Field, we extract critical exponents for the planar cri…
The Wulff crystal of self-dual FK-percolation becomes round when approaching criticality
Ioan Manolescu, Maran Mohanarangan
The study of the phase transition in planar FK-percolation on the square lattice has seen significant recent breakthroughs. The model undergoes a change in the nature of its phase…
Comparison of arm exponents in planar FK-percolation
Loïc Gassmann, Ioan Manolescu
By the FKG inequality for FK-percolation, the probability of the alternating two-arm event is smaller than the product of the probabilities of having a primal arm and a dual arm, r…
Exploring the phase transition of planar FK-percolation
Ioan Manolescu
The aim of these notes is to give a quick introduction to FK-percolation, focusing on certain recent results about the phase transition of the two dimensional model, namely its con…