Chaos in the Z(2) Gauge Model on a Generalized Bethe Lattice of Plaquettes

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.