Locally representable one-parameter automorphism groups of AF algebras and KMS states

As a mathematical model of classical statistical lattice systems we consider locally representable one-parameter automorphism groups of AF (approximately finite-dimensional) C∗-algebras. We demonstrate how to construct examples which exhibit various types of non uniqueness of equilibrium states (or KMS states). Towards the classification problem of cocycle-conjugacy classes of one-parameter automorphism groups in general we introduce a new invariant called marginal spectrum (associated with ground states) and apply it to a special case of infinite tensor product type actions.