Critical percolation in the dynamics of the 2d ferromagnetic Ising model

Understand

We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase.

• We evolve the system with kinetic Monte Carlo rules that do not conserve the order parameter.
• We confirm the rapid approach to random critical percolation in a time-scale that diverges with the system size but is much shorter than the equilibration time.
• We study the scaling properties of the evolution towards critical percolation and we identify an associated growing length, different from the curvature driven one.