Low-temperature 2D Ising Glauber dynamics from sufficiently biased random initializations rapidly orders into the plus phase for every temperature above critical.
Mixing in time and space for lattice spin systems: A combinatorial view.Random Structures & Algorithms, 24(4):461–479
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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.