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$N^{1/3}$ scaling in the 2D Ising model and the Airy diffusion

Ergodic Theory & Statistical Mechanics

$N^{1/3}$ scaling in the 2D Ising model and the Airy diffusion

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Senya Shlosman , Center for Theoretical Physics, France
Fine Hall 601

I will consider the behavior of the phase separation interface of the 2D Ising model in the vicinity of the wall. Properly scaled, it converges to the diffusion process, with a drift expressed via Airy function. This process has appeared first in Ferrari&Spohn's study of Brownian motion, constrained to stay outside circular barrier. Joint work with D. Ioffe and Y. Velenik.