Anomalous Ising freezing times

We measure the relaxation time of a square lattice Ising ferromagnet that is quenched to zero-temperature from supercritical initial conditions. We reveal an anomalous and seemingly overlooked timescale associated with the relaxation to "frozen" two-stripe states. While close to a power law of the form $\sim L^{\nu}$ , we argue this timescale actually grows as $\sim L^{2}\ln L$, with L the linear dimension of the system. We uncover the mechanism behind this scaling form by using a synthetic initial condition that replicates the late time ordering of two-stripe states, and subsequently explain it heuristically.