Speaker:

Eyal Lubetzky

Title:

The (2+1)-dimensional SOS model: limiting shape and dynamics

Abstract:

We present new results on the (2+1)-dimensional Solid-On-Solid model at low temperatures (also known as the Onsager-Temperley sheet, introduced in the 1950's). Bricmont, El-Mellouki and Froelich (1986) showed that in the presence of a floor there is an entropic repulsion phenomenon, lifting the surface to a height which is logarithmic in the side of the box. We refine this and establish the typical height of the SOS surface is precisely the floor of [1/(4 beta) log n], where n is the side-length of the box and beta is the inverse-temperature. We proceed to study the level lines of the surface, and among other results show that the highest one has cube-root fluctuations from the side boundaries. As a consequence of these results, and in contrast to the 1D behavior, the Glauber dynamics for SOS is exponentially slow, as it passes through a series of meta-stable states where it needs to create macroscopic droplets in order to rise from an initially flat configuration to its final height.

Based on joint works with Pietro Caputo, Fabio Martinelli, Fabio Toninelli and Allan Sly.