Formation of facets for an effective model of crystal growth

Dmitry Ioffe, Senya Shlosman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationSojourns in Probability Theory and Statistical Physics - I - Spin Glasses and Statistical Mechanics, A Festschrift for Charles M. Newman
EditorsVladas Sidoravicius
PublisherSpringer
Pages199-245
Number of pages47
ISBN (Print)9789811502934
DOIs
Publication statusPublished - 2019
EventInternational Conference on Probability Theory and Statistical Physics, 2016 - Shanghai, China
Duration: 25 Mar 201627 Mar 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume298
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Probability Theory and Statistical Physics, 2016
Country/TerritoryChina
CityShanghai
Period25/03/1627/03/16

Keywords

  • Equilibrium crystal shapes
  • Infinite sequence of first order transitions
  • Microscopic facets
  • SOS model with bulk fields

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