  Low temperature dynamics of Ising ferromagnets under finite magnetic fields
are studied in terms of quantum spin representations of stochastic evolution
operators. These are constructed for the Glauber dynamic as well as for a
modification of this latter, introduced by K. Park {\it et al.} in Phys. Rev.
Lett. {\bf 92}, 015701 (2004). In both cases the relaxation time after a field
quench is evaluated both numerically and analytically using the spectrum gap of
the corresponding operators. The numerical work employs standard recursive
techniques following a symmetrization of the evolution operator accomplished by
a non-unitary spin rotation. The analytical approach uses low temperature
limits to identify dominant terms in the eigenvalue problem. It is argued that
the relaxation times already provide a measure of actual nucleation lifetimes
under finite fields. The approach is applied to square, triangular and
honeycomb lattices.
