Yoshida, Nobuo The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice. (English) Zbl 0992.60089 Ann. Inst. Henri Poincaré, Probab. Stat. 37, No. 2, 223-243 (2001). For ferromagnetic spin systems on the \(d\)-dimensional integer lattice (\(d\geq 1\)) with compact spin space, D. W. Stroock and 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. Reviewer: Ostap Hryniv (Cambridge) Cited in 22 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:ferromagnetic systems; unbounded spins; log-Sobolev inequality; Poincaré inequality; exponential decay of spin-spin correlations; mixing condition Citations:Zbl 0745.60104; Zbl 0758.60070 PDFBibTeX XMLCite \textit{N. Yoshida}, Ann. Inst. Henri Poincaré, Probab. Stat. 37, No. 2, 223--243 (2001; Zbl 0992.60089) Full Text: DOI Numdam EuDML