• DOI:10.1007/978-1-4939-0339-9_4
• Corpus ID: 117912367

The Scaling Limit for Zero-Temperature Planar Ising Droplets: With and Without Magnetic Fields

@article{Lacoin2014TheSL,
  title={The Scaling Limit for Zero-Temperature Planar Ising Droplets: With and Without Magnetic Fields},
  author={Hubert Lacoin},
  journal={arXiv: Probability},
  year={2014},
  pages={85-120}
}

• H. Lacoin
• Published 9 October 2012
• Physics, Mathematics
• arXiv: Probability

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.