We consider a general class of Glauber dynamics reversible with respect to the
standard Ising model in Z^d with zero external field and inverse temperature b
strictly larger than the critical value b_c in dimension 2 or the so called 'slab
threshold' bˆ_c in dimension d >= 3. We first prove that the inverse spectral gap in
a large cube of side N with plus boundary conditions is, apart from logarithmic
corrections, larger than N in d=2 while the logarithmic Sobolev constant is
instead larger than N^2 in any dimension.