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The scaling limit of critical Ising interfaces is CLE(3)
Stéphane Benoist, Clément Hongler
In this paper, we consider the set of interfaces between + and - spins arising for the critical planar Ising model on a domain with + boundary conditions, and show that it converge…
Conformal invariance of crossing probabilities for the Ising model with free boundary conditions
Stéphane Benoist, Hugo Duminil-Copin, Clément Hongler
We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigat…
Crossing probabilities in topological rectangles for the critical planar FK-Ising model
Dmitry Chelkak, Hugo Duminil-Copin, Clément Hongler
We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundar…
Ising Interfaces and Free Boundary Conditions
Clément Hongler, Kalle Kytölä
We study the interfaces arising in the two-dimensional Ising model at critical temperature, without magnetic field. We show that in the presence of free boundary conditions between…
Connection probabilities and RSW-type bounds for the FK Ising model
Hugo Duminil-Copin, Clément Hongler, Pierre Nolin
We prove Russo-Seymour-Welsh-type uniform bounds on crossing probabilities for the FK Ising model at criticality, independent of the boundary conditions. Our proof relies mainly on…
Critical percolation: the expected number of clusters in a rectangle
Clément Hongler, Stanislav Smirnov
We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In particular the expected number of clusters se…