Low-temperature 2D Ising Glauber dynamics from sufficiently biased random initializations rapidly orders into the plus phase for every temperature above critical.
Glauber dynamics on trees and hyperbolic graphs.Probability Theory and Related Fields, 131(3):311–340
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Rapid phase ordering of Ising dynamics on $\mathbb Z^2$
Low-temperature 2D Ising Glauber dynamics from sufficiently biased random initializations rapidly orders into the plus phase for every temperature above critical.