  We consider a one-dimensional lattice system of unbounded, real-valued spins
with arbitrary strong, quadratic, finite-range interaction. We show that the
canonical ensemble (ce) satisfies a uniform logarithmic Sobolev inequality
(LSI). The LSI constant is uniform in the boundary data, the external field and
scales optimally in the system size. This extends a classical result of H.T.
Yau from discrete to unbounded, real-valued spins. It also extends prior
results of Landim, Panizo & Yau or Menz for unbounded, real-valued spins from
absent- or weak- to strong-interaction. The proof of the LSI uses a combination
of the two-scale approach and a block-decomposition technique introduced by
Zegarlinski. Main ingredients are the strict convexity of the coarse-grained
Hamiltonian, the equivalence of ensembles and the decay of correlations in the
ce. Those ingredients were recently provided by the authors.
