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Zero-temperature 2D Ising model and anisotropic curve-shortening flow
[article]
2013
arXiv
pre-print
Let be a simply connected, smooth enough domain of ^2. For L>0 consider the continuous time, zero-temperature heat bath dynamics for the nearest-neighbor Ising model on Z^2 with initial condition such that σ_x=-1 if x∈ L and σ_x=+1 otherwise. It is conjectured cf:Spohn that, in the diffusive limit where space is rescaled by L, time by L^2 and L→∞, the boundary of the droplet of "-" spins follows a deterministic anisotropic curve-shortening flow, where the normal velocity at a point of its
arXiv:1112.3160v2
fatcat:s53txnxjw5cpjlbi3vl7dchazq