TY - GEN

T1 - Formation of facets for an effective model of crystal growth

AU - Ioffe, Dmitry

AU - Shlosman, Senya

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Equilibrium crystal shapes

KW - Infinite sequence of first order transitions

KW - Microscopic facets

KW - SOS model with bulk fields

UR - http://www.scopus.com/inward/record.url?scp=85077686515&partnerID=8YFLogxK

U2 - 10.1007/978-981-15-0294-1_9

DO - 10.1007/978-981-15-0294-1_9

M3 - Conference contribution

AN - SCOPUS:85077686515

SN - 9789811502934

T3 - Springer Proceedings in Mathematics and Statistics

SP - 199

EP - 245

BT - Sojourns in Probability Theory and Statistical Physics - I - Spin Glasses and Statistical Mechanics, A Festschrift for Charles M. Newman

A2 - Sidoravicius, Vladas

PB - Springer

T2 - International Conference on Probability Theory and Statistical Physics, 2016

Y2 - 25 March 2016 through 27 March 2016

ER -