  We investigate the Z(2) gauge model on a generalized Bethe lattice with three
plaquette representation of the action. We obtain the cascade of phase
transitions according to Feigenbaum scheme leading to chaotic states for some
values of parameters of the model. The duality between this gauge model and
three site Ising spin model on Husimi tree is shown. The Lyapunov exponent as a
new order parameter for the characterization of the model in the chaotic region
is considered. The line of the second order phase transition, which corresponds
to the points of the first period doubling bifurcation, is also obtained.
