  We study a spatially extended model of noise-induced magnetization reversal:
a classical Ginzburg-Landau theory, restricted to a bounded interval and
perturbed by weak spatiotemporal noise. We compute the activation barrier and
Kramers prefactor. As the interval length increases, a transition between
activation regimes occurs, at which the prefactor diverges. We relate this to
transitions that occur in low-temperature quantum field theory.
