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.
- Coarsening models
- Random environment
- Zero-temperature Glauber dynamics
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics