Geodesic
Zero-temperature 2D stochastic Ising model and anisotropic curve-shortening flow
Journal of the European Mathematical Society, Tome 16 (2014) no. 12, pp. 2557-2615

Voir la notice de l'article provenant de la source EMS Press

Let D be a simply connected, smooth enough domain of R2. For L>0 consider the continuous time, zero-temperature heat bath dynamics for the nearest-neighbor Ising model on Z2 with initial condition such that σx​=−1 if x∈LD and σx​=+1 otherwise. It is conjectured [23] that, in the diffusive limit where space is rescaled by L, time by L2 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 boundary is given by the local curvature times an explicit function of the local slope. The behavior should be similar at finite temperature T​, with a different temperature-dependent anisotropy function.
DOI : 10.4171/jems/493
Classification : 60-XX, 00-XX, 82-XX
Keywords: Ising model, Glauber dynamics, curve-shortening flow 
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     title = {Zero-temperature {2D} stochastic {Ising} model and anisotropic curve-shortening flow},
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Hubert Lacoin; François Simenhaus; Fabio L. Toninelli. Zero-temperature 2D stochastic Ising model and anisotropic curve-shortening flow. Journal of the European Mathematical Society, Tome 16 (2014) no. 12, pp. 2557-2615. doi: 10.4171/jems/493

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