  We investigate the properties of the Ising-Glauber model on a periodic cubic
lattice of linear dimension L after a quench to zero temperature. The resulting
evolution is extremely slow, with long periods of wandering on constant energy
plateaux, punctuated by occasional energy-decreasing spin-flip events. The
characteristic time scale tau for this relaxation grows exponentially with the
system size; we provide a heuristic and numerical evidence that tau exp(L^2).
For all but the smallest-size systems, the long-time state is almost never
static. Instead the system contains a small number of "blinker" spins that
continue to flip forever with no energy cost. Thus the system wanders ad
infinitum on a connected set of equal-energy blinker states. These states are
composed of two topologically complex interwoven domains of opposite phases.
The average genus g_L of the domains scales as L^gamma, with gamma~1.7; thus
domains typically have many holes, leading to a "plumber's nightmare" geometry.
