2019/10/17 by Younghak Kwon, Jaehun Lee, Kwon, Younghak +3
Mathematics · #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1910.07702
arxiv created 2019/11/30 · arxiv updated 2019/12/03
We consider a one-dimensional lattice system of unbounded, real-valued spins with arbitrary strong, quadratic, finite-range interaction. We show the equivalence of the grand canonical ensemble (gce) and the canonical ensemble (ce), in the sense of observables and correlations. A direct consequence is that the correlations of the ce decay exponentially plus a volume correction term. The volume correction term is uniform in the external field, the mean spin and scales optimally in the system size. This extends prior results of Cancrini & Martinelli for bounded discrete spins to unbounded continuous spins. The result is obtained by adapting Cancrini & Martinelli's method combined with authors' recent approach on continuous real-valued spin systems.