I will discuss the fate of Ising ferromagnets endowed with a zero-temperature non-conservative dynamics, both the microscopic spin-flip dynamics and the macroscopic dynamics based on the time-dependent Ginzburg-Landau equation. After reviewing the situation in three dimensions, I will present evidence of a deep connection between the zero-temperature coarsening of both the two-dimensional time-dependent Ginzburg-Landau equation and the kinetic Ising model with critical continuum percolation. This connection allows to predict the probabilities of reaching a variety of topologically distinct metastable stripe states as these probabilities turn out to be related with crossing probabilities from critical percolation.

Department of Physics, Boston University, Boston and IPhT