The logarithmic sobolev inequality for discrete spin systems on a lattice

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.During the period of this research, both authors were partially supported by NSF grant DMS 8913328