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

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

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Senya Shlosman, CPT, Univ. Marseille, Luminy
Jadwin Hall 343

For the two-dimensional Ising model at low temperatures consider a floating droplet of the (+) phase floating in the sea of (-) phase, pressed against a horizontal wall within a box of linear size N. I will explain that the fluctuations of the boundary of the droplet near the contact with the wall are of the order of N^{1/3}. When scaled by N^{1/3} vertically and by N^{2/3} horizontally, the limiting behavior of the boundary as N goes to infinity is given by the Airy diffusion process. This diffusion process has appeared earlier in a paper by Ferrari and Spohn, where the brownian motion above the parabolic barrier is considered. Work in progress with D. Ioffe and Y. Velenik.