Coarsening Dynamics on Zd with Frozen Vertices

M. Damron, S. M. Eckner, H. Kogan, C. M. Newman, V. Sidoravicius

Research output: Contribution to journalArticle

Abstract

We study Markov processes in which ±1-valued random variables σx(t),x∈Zd, update by taking the value of a majority of their nearest neighbors or else tossing a fair coin in case of a tie. In the presence of a random environment of frozen plus (resp., minus) vertices with density ρ+ (resp., ρ-), we study the prevalence of vertices that are (eventually) fixed plus or fixed minus or flippers (changing forever). Our main results are that, for ρ+>0 and ρ-=0, all sites are fixed plus, while for ρ+>0 and ρ- very small (compared to ρ+), the fixed minus and flippers together do not percolate. We also obtain some results for deterministic placement of frozen vertices.

Original languageEnglish (US)
Pages (from-to)60-72
Number of pages13
JournalJournal of Statistical Physics
Volume160
Issue number1
DOIs
StatePublished - Jul 23 2015

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Keywords

  • Coarsening models
  • Random environment
  • Zero-temperature Glauber dynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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