The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice

We consider a ferromagnetic spin system with unbounded spin spaces on the d-dimensional integer lattice (d greater than or equal to 1). We prove the equivalence of the log-Sobolev inequality, Poincare inequality, and the exponential decay of the spin-spin correlation, which was originally obtained by D.W. Stroock and B. Zegarlinski [23,24] in the compact spin space setting. (C) 2001 Editions scientifiques et medicales Elsevier SAS.