  When a two-dimensional Ising ferromagnet is quenched from above the critical
temperature to zero temperature, the system eventually converges to either a
ground state (all spins aligned) or an infinitely long-lived metastable stripe
state. By applying results from percolation theory, we analytically determine
the probability to reach the stripe state as a function of the aspect ratio and
the form of the boundary conditions. These predictions agree with simulation
results. Our approach generally applies to coarsening dynamics of non-conserved
scalar fields in two dimensions.
