  We consider Markov random fields of discrete spins on the lattice $\Zd$. We
use a technique of coupling of conditional distributions. If under the coupling
the disagreement cluster is "sufficiently" subcritical, then we prove the
Poincar\'e inequality. In the whole subcritical regime, we have a weak
Poincar\'e inequality and corresponding polynomial upper bound for the
relaxation of the associated Glauber dynamics.
