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Zbl 0992.60089
Yoshida, Nobuo
The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 37, No.2, 223-243 (2001). ISSN 0246-0203

For ferromagnetic spin systems on the $d$-dimensional integer lattice ($d\ge 1$) with compact spin space, {\it D. W. Stroock} and {\it 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.
[Ostap Hryniv (Cambridge)]

MSC 2000:: *60K35 Interacting random processes
82B20 Lattice systems

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

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