  The Q- state Potts model on the Bethe lattice is investigated for Q<2. The
magnetization of this model exhibits a complicated behavior including both the
period doubling bifurcation and chaos. The Lyapunov exponents of the
Potts-Bethe map are considered as order parameters. We find a scaling behavior
in the distribution of Lyapunov exponents in fully developed chaotic case.
Using the thermodynamic formalism of dynamical systems have we investigated the
nonanalytic behavior in the distribution of Lyapunov exponents and located the
point of phase transition of the ''chaotic free energy''.
