Abstract
For finite range lattice gases with a finite spin space, it is shown that the Dobrushin-Shlosman mixing condition is equivalent to the existence of a logarithmic Sobolev inequality for the associated (unique) Gibbs state. In addition, implications of these considerations for the ergodic properties of the corresponding Glauber dynamics are examined.
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Communicated by Ya.G. Sinai
During the period of this research, both authors were partially supported by NSF grant DMS 8913328
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Stroock, D.W., Zegarlinski, B. The logarithmic sobolev inequality for discrete spin systems on a lattice. Commun.Math. Phys. 149, 175–193 (1992). https://doi.org/10.1007/BF02096629
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DOI: https://doi.org/10.1007/BF02096629