Fixation for coarsening dynamics in 2D slabs

Michael Damron, Hana Kogan, Charles Newman, Vladas Sidoravicius

Research output: Contribution to journalArticle

Abstract

We study zero-temperature Ising Glauber Dynamics, on 2D slabs of thickness k≥2. In this model, ±1-valued spins at integer sites update according to majority vote dynamics with two opinions. We show that all spins reaches a final state (that is, the system fixates) for k=2 under free boundary conditions and for k=2 or 3 under periodic boundary conditions. For thicker slabs there are sites that fixate and sites that do not.

Original languageEnglish (US)
Article number105
JournalElectronic Journal of Probability
Volume18
DOIs
StatePublished - Dec 17 2013

Fingerprint

Coarsening
Fixation
Glauber Dynamics
Vote
Periodic Boundary Conditions
Free Boundary
Ising
Update
Boundary conditions
Integer
Zero
Model
Temperature
Free boundary

Keywords

  • Coarsening
  • Glauber dynamics
  • Ising model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Fixation for coarsening dynamics in 2D slabs. / Damron, Michael; Kogan, Hana; Newman, Charles; Sidoravicius, Vladas.

In: Electronic Journal of Probability, Vol. 18, 105, 17.12.2013.

Research output: Contribution to journalArticle

Damron, Michael ; Kogan, Hana ; Newman, Charles ; Sidoravicius, Vladas. / Fixation for coarsening dynamics in 2D slabs. In: Electronic Journal of Probability. 2013 ; Vol. 18.
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