If I understood this correctly, the Gibbs Specification for the Ising model on $ℤ^d$ dos not have a unique Gibbs Measure for β above the critical level. But what about the Ising model on a finite lattice $V⊂ℤ^d$?

And if it is not unique for a finite lattice, how is that possible as I can construct a Gibbs Sampler – a markov chain, that has the measure that fulfills the specification as its stationary distribution – that is clearly irreducible (we can go from anywhere to the $\{-1\}^V$ state and get everywhere from there) and thus must have an unique stationary distribution?