  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.
