6 citations · 6 across the 2 of their papers we have counts for
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Existence of phase transition for percolation using the Gaussian Free Field
Hugo Duminil-Copin, Subhajit Goswami, Aran Raoufi +2
In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension undergoes a non-trivial phase transition (in the sense that ).…
Subcritical phase of -dimensional Poisson-Boolean percolation and its vacant set
Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion
We prove that the Poisson-Boolean percolation on undergoes a sharp phase transition in any dimension under the assumption that the radius distribution has a f…
Translation-Invariant Gibbs States of Ising model: General Setting
Aran Raoufi
We prove that at any inverse temperature and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations…
Exponential decay of connection probabilities for subcritical Voronoi percolation in
Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion
We prove that for Voronoi percolation on , there exists such that - for , there exists such that $\mathbb{P}_p[0\text{ connected to dista…
Indicable groups and
Aran Raoufi, Ariel Yadin
A conjecture of Benjamini & Schramm from 1996 states that any finitely generated group that is not a finite extension of Z has a non-trivial percolation phase. Our main results pro…
A note on continuity of magnetization at criticality for the ferromagnetic Ising model on amenable quasi-transitive graphs with exponential growth
Aran Raoufi
The purpose of this modest note is to point out that the proof of the recent result of Huchcroft concerning continuity of phase transition in Bernoulli percolation is applicable to…