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math.PR2025
Planar percolation and the loop O(n) model
Alexander Glazman, Matan Harel, Nathan Zelesko
We show that a large class of site percolation processes on any planar graph contains either zero or infinitely many infinite connected components. The assumptions that we require…
math.PR2025
Discontinuous transition in 2D Potts: I. Order-Disorder Interface convergence
Moritz Dober, Alexander Glazman, Sébastien Ott
We study a -state Potts model on the square grid when at the point of its (discontinous) transition. This model exhibits exactly extremal Gibbs measures: $q…