We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are suitable approximations of smooth domains. A specific spatial average of the derivative at time 0 of the volume variation of a droplet close to a boundary point is equal to its curvature multiplied by a direction dependent coefficient. We compute the explicit value of this coefficient.
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Cerf, R., Louhichi, S. The Initial Drift of a 2D Droplet at Zero Temperature. Probab. Theory Relat. Fields 137, 379–428 (2007). https://doi.org/10.1007/s00440-006-0007-4
- 2D Ising model
- Glauber dynamics
- Zero temperature
- Markov process
- Mean curvature
Mathematics Subject Classification (2000)