1 citations · 2 across the 18 of their papers we have counts for
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An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions
Hugo Duminil-Copin, Romain Panis
This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions . Among other results, we obtain up-to-constant estimate…
An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions
Hugo Duminil-Copin, Romain Panis
This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions . We obtain an upper bound for the full-space…
The incipient infinite cluster of the FK-Ising model in dimensions and the susceptibility of the high-dimensional Ising model
Romain Panis
We consider the critical FK-Ising measure on with . We construct the measure $ϕ^\infty:=\lim_{|x|\rightarrow \infty}ϕ_{β_c}[\:\cdot\: |\: 0\leftrig…
The torus plateau for the high-dimensional Ising model
Yucheng Liu, Romain Panis, Gordon Slade
We consider the Ising model on a -dimensional discrete torus of volume , in dimensions and for large , in the vicinity of the infinite-volume critical point .…
New lower bounds for the (near) critical Ising and models' two-point functions
Hugo Duminil-Copin, Romain Panis
We study the nearest-neighbour Ising and models on with and obtain new lower bounds on their two-point functions at (and near) criticality. Together w…