Chaotic Repellers in Antiferromagnetic Ising Model

Abstract

For the first time we present the consideration of the antiferromagnetic Ising model in case of fully developed chaos and obtain the exact connection between this model and chaotic repellers. We describe the chaotic properties of this statistical mechanical system via the invariants characterizing a fractal set and show that in chaotic region it displays phase transition at {\it positive} "temperature" $ \beta_c = 0.89 $. We obtain the density of the invariant measure on the chaotic repeller.