Communications in Mathematical Physics

, Volume 149, Issue 1, pp 175–193

The logarithmic sobolev inequality for discrete spin systems on a lattice


  • Daniel W. Stroock
    • Department of Mathematics, 2-272M.I.T.
  • Boguslaw Zegarlinski
    • Department of Mathematics, 2-272M.I.T.
    • Fakultät für MathematikRuhr-Universität-Bochum

DOI: 10.1007/BF02096629

Cite this article as:
Stroock, D.W. & Zegarlinski, B. Commun.Math. Phys. (1992) 149: 175. doi:10.1007/BF02096629


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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© Springer-Verlag 1992