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Decay of correlations and uniqueness of the infinite-volume Gibbs measure of the canonical ensemble of 1d-lattice systems. (arXiv:1807.03891v1 [math.PR])
来源于:arXiv
We consider a one-dimensional lattice system of unbounded, real-valued spins
with arbitrary strong, quadratic, finite-range interaction. We show the
equivalence of cor- relations of the grand canonical (gce) and the canonical
ensemble (ce). As a corollary we obtain that the correlations of the ce decay
exponentially plus a volume correction term. Then, we use the decay of
correlation to verify a conjecture that the infinite-volume Gibbs measure of
the ce is unique on a one-dimensional lattice. For the equivalence of
correlations, we modify a method that was recently used to show the equivalence
of the ce and the gce on the level of thermodynamic functions. In this article
we also show that the equivalence of the ce and the gce holds on the level of
observables. One should be able to extend the methods and results to graphs
with bounded degree as long as the gce has a sufficient strong decay of
correlations. 查看全文>>