1210.2597 (Hubert Lacoin)

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

Hubert Lacoin

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.

View original: http://arxiv.org/abs/1210.2597