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Chapitre D'ouvrage Année : 2015

The scaling limit for zero temperature planar Ising droplets: with and without magnetic fields

Résumé

We consider the continuous time, zero-temperature heat-bath dynamics for the nearest-neighbor Ising model on $Z^2$ with positive magnetic field. For a system of size $L\in N$, we start with initial condition $\sigma$ such that $\sigma_x=-1$ if $x\in[-L,L]^2$ and $\sigma_x=+1$ and investigate the scaling limit of the set of $-$ spins when both time and space are rescaled by $L$. We compare the obtained result and its proof with the case of zero-magnetic fields, for which a scaling result was proved in arXiv:1112.3160. In that case, the time-scaling is diffusive and the scaling limit is given by anisotropic motion by curvature.

Dates et versions

hal-00922725 , version 1 (30-12-2013)

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Citer

Hubert Lacoin. The scaling limit for zero temperature planar Ising droplets: with and without magnetic fields. Topics in Percolative and Disordered Systems, 2015, ⟨10.1007/978-1-4939-0339-9_4⟩. ⟨hal-00922725⟩
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