Appears in collection : 100 (102!) Years of the Ising Model

Fifty years ago, Dobrushin famously showed that the 3D Ising interface on a cylinder with plus/minus boundary condition is rigid. By now there is detailed understanding of the (2+1)D Solid-On-Solid model that approximates said interface, and notably, its entropic repulsion phenomenon above a hard wall. We will discuss the picture in the SOS approximation and recent progress on confirming these predictions for the 3D Ising model.

Based on joint works with Caputo, Martinelli, Toninelli and Sly on the SOS model, and with Gheissari on the 3D Ising model.