  In this Letter, we use a general renormalization-group algorithm to implement
Propp and Wilson's "coupling from the past" approach to complex physical
systems. Our algorithm follows the evolution of the entire configuration space
under the Markov chain Monte Carlo dynamics from parts of the configurations
(patches) on increasing length scales, and it allows us to generate "exact
samples" of the Boltzmann distribution, which are rigorously proven to be
uncorrelated with the initial condition. We validate our approach in the
two-dimensional Ising spin glass on lattices of size 64 x 64.
