  We investigate the metastable behavior of reversible Markov chains on
possibly countable infinite state spaces. Based on a new definition of
metastable Markov processes, we compute precisely the mean transition time
between metastable sets. Under additional size and regularity properties of
metastable sets, we establish asymptotic sharp estimates on the Poincar\'e and
logarithmic Sobolev constant. The main ingredient in the proof is a capacitary
inequality along the lines of V. Maz'ya that relates regularity properties of
harmonic functions and capacities. We exemplify the usefulness of this new
definition in the context of the random field Curie-Weiss model, where
metastability and the additional regularity assumptions are verifiable.
