Gibbs states for AF algebras

We consider a special class of C*-systems containing asymptotically Abelian binary shifts and shifts of Temperley-Lieb algebras. We study Gibbs states for these systems corresponding to potentials with finite range interaction, and obtain the same results as the well-known Araki's results for a one-dimensional quantum lattice. In particular, it is proved that a Gibbs state in the infinite volume is a translation invariant KMS state having the exponential uniform clustering property. Entropic properties of the Gibbs states are also discussed. This allows us, in particular, to construct new examples of quantum K-systems. (C) 1998 American Institute of Physics. [S0022-2488(98)01112-8].