115 citations · 1.2k across the 68 of their papers we have counts for
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The critical temperature for the Ising model on planar doubly periodic graphs
David Cimasoni, Hugo Duminil-Copin
We provide a simple characterization of the critical temperature for the Ising model on an arbitrary planar doubly periodic weighted graph. More precisely, the critical inverse tem…
Lectures on Self-Avoiding Walks
Roland Bauerschmidt, Hugo Duminil-Copin, Jesse Goodman +1
These lecture notes provide a rapid introduction to a number of rigorous results on self-avoiding walks, with emphasis on the critical behaviour. Following an introductory overview…
Self-avoiding walk is sub-ballistic
Hugo Duminil-Copin, Alan Hammond
We prove that self-avoiding walk on Z^d is sub-ballistic in any dimension d at least two. That is, writing ||u|| for the Euclidean norm of u \in Z^d, and SAW_n for the uniform meas…
On the Gibbs states of the noncritical Potts model on Z^2
Loren Coquille, Hugo Duminil-Copin, Dmitry Ioffe +1
We prove that all Gibbs states of the q-state nearest neighbor Potts model on Z^2 below the critical temperature are convex combinations of the q pure phases; in particular, they a…