Low-temperature 2D Ising Glauber dynamics from sufficiently biased random initializations rapidly orders into the plus phase for every temperature above critical.
Invariance principle for a Potts interface along a wall.Journal of Statistical Physics, 180(1):832–861
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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.