  We consider Glauber dynamics reversible with respect to Gibbs measures with
heavy tails. Spins are unbounded. The interactions are bounded and finite
range. The self potential enters into two classes of measures, $\kappa$-concave
probability measure and sub-exponential laws, for which it is known that no
exponential decay can occur. We prove, using coercive inequalities, that the
associated infinite volume semi-group decay to equilibrium polynomially and
stretched exponentially, respectively. Thus improving and extending previous
results by Bobkov and Zegarlinski.
