  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.
