  We consider the stochastic dynamics of Ising ferromagnets (either pure or
random) near zero temperature. The master equation satisfying detailed balance
can be mapped onto a quantum Hamiltonian which has an exact zero-energy ground
state representing the thermal equilibrium. The largest relaxation time
$t_{eq}$ governing the convergence towards this Boltzmann equilibrium in
finite-size systems is determined by the lowest non-vanishing eigenvalue
$E_1=1/t_{eq}$ of the quantum Hamiltonian $H$. We introduce and study a
real-space renormalization procedure for the quantum Hamiltonian associated to
the single-spin-flip dynamics of Ising ferromagnets near zero temperature. We
solve explicitly the renormalization flow for two cases. (i) For the
one-dimensional random ferromagnetic chain with free boundary conditions, the
largest relaxation time $t_{eq}$ can be expressed in terms of the set of random
couplings for various choices of the dynamical transition rates. The validity
of these RG results in $d=1$ is checked by comparison with another approach.
(ii) For the pure Ising model on a Cayley tree of branching ratio $K$, we
compute the exponential growth of $t_{eq}(N)$ with the number $N$ of
generations.
