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… 
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