(i.e., chosenindependently of the randomness) subsequence of finite-volume Gibbs distributions.

It was proved for Euclidean lattices that there alwaysexists a deterministic subsequence along which the Newman-Stein andAizenman-Wehr constructions result in the same metastate. The metastate isespecially useful in systems where deterministic sequences of volumes failto converge to a thermodynamic state, and/or there are many competingobservable thermodynamic