Convergence of Ising interfaces to Schramm’s SLE curves. (Convergence des interfaces d’Ising vers les courbes SLE introduites par Schramm.) (English. French summary) Zbl 1294.82007

The authors consider spin Ising and the Fortuin-Kasteleyn (FK)-Ising models on the square lattice \(\mathbb{Z}^2,\) where the FK-Ising model is its random-cluster counterpart. The strong convergence of the interfaces in the planar critical Ising model is proved and its random-cluster representation of Schramm-Loewner evolution curves with the parameters \(k=3\) and \(k=16/3,\) respectively.


82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
60J67 Stochastic (Schramm-)Loewner evolution (SLE)
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B27 Critical phenomena in equilibrium statistical mechanics
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