LA Probability Forum

We will discuss recent progress on understanding the entropic repulsion phenomenon for low-temperature 3D Ising interfaces. More precisely, if one considers the low-temperature Ising model in a box of side-length n in three dimensions, with Dobrushin's boundary conditions (plus below the xy-plane and minus above), then the interface separating the predominantly plus region from the predominantly minus region is localized about height zero (independently of n). Suppose one conditions on this interface staying entirely above a hard barrier at height -k_n: when k_n is large enough, the barrier effect is not significant and the interface remains localized, but when k_n is zero, say, it causes the entire interface to lift off and have diverging average height. We will describe recent work joint with Eyal Lubetzky identifying the critical k_n* delineating this localization/delocalization transition.