The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice (Q5937483)

For ferromagnetic spin systems on the \(d\)-dimensional integer lattice (\(d\geq 1\)) with compact spin space, \textit{D. W. Stroock} and \textit{B. Zegarlinski} [Commun. Math. Phys. 144, No. 2, 303-323 (1992; Zbl 0745.60104) and ibid. 149, No. 1, 175-193 (1992; Zbl 0758.60070)] showed that the log-Sobolev inequality, the Poincaré inequality, and the exponential decay of spin-spin correlations are equivalent. In the present paper the author extends their results to ferromagnetic systems of unbounded spins. The obtained inequalities hold uniformly in volume and boundary condititions.