By Dmitry Ioffe, Technion, Haifa

We consider a version of low temperature solid on solid 2+1 random
interface coupled with high and low density bulk Bernoulli fields, which is intended
to model flat faces of microscopic Wulff crystals in three dimensional Ising model.
As the total number of particles in the bulk is tuned, the surface undergoes an infinite
sequence of first order transitions, which correspond to spontaneous creation of macroscopic
size facets. The 1/3-scaling behaviour of ensembles of microscopic level lines along edges
of the confining box is also discussed.

Based on joint works with Senya Shlosman, Yvan Velenik and Vitali Wachtel.