  We model magnetization processes that take place through tunneling in
crystals of single-molecule magnets, such as Mn_12 and Fe_8. These processes
take place when a field H is applied after quenching to very low temperatures.
Magnetic dipolar interactions and spin flipping rules are essential ingredients
of the model. The results obtained follow from Monte Carlo simulations and from
the stochastic model we propose for dipole field diffusion. Correlations
established before quenching are shown to later drive the magnetization
process. We also show that in simple cubic lattices, m \propto sqrt(t) at time
t after H is applied, as observed in Fe_8, but only for 1+2\log_10(h_d/h_w)
time decades, where h_d is some near-neighbor magnetic dipolar field and a spin
reversal can occur only if the magnetic field acting on it is within some field
window (-h_w,h_w). However, the sqrt(t) behavior is not universal. For BCC and
FCC lattices, m \propto t^p, but p \simeq 0.7 . An expression for p in terms of
lattice parameters is derived. At later times the magnetization levels off to a
constant value. All these processes take place at approximately constant
magnetic energy if the annealing energy epsilon_a is larger than the tunneling
window's energy width (i.e., if epsilon_a \gtrsim g\mu_B h_w S). Thermal
processes come in only later on to drive further magnetization growth.
