  We study an effective model of microscopic facet formation for low
temperature three dimensional microscopic Wulff crystals above the droplet
condensation threshold. The model we consider is a 2+1 solid on solid surface
coupled with high and low density bulk Bernoulli fields. At equilibrium the
surface stays flat. Imposing a canonical constraint on excess number of
particles forces the surface to "grow" through the sequence of spontaneous
creations of macroscopic size monolayers. We prove that at all sufficiently low
temperatures, as the excess particle constraint is tuned, the model undergoes
an infinite sequence of first order transitions, which traces an infinite
sequence of first order transitions in the underlying variational problem. Away
from transition values of canonical constraint we prove sharp concentration
results for the rescaled level lines around solutions of the limiting
variational problem.
