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 in the presence of a three-plaquette interaction. We obtain a cascade of phase transitions according to the Feigenbaum scheme leading to chaotic states for some values of parameters of the model. The duality between this gauge model and the three-site Ising spin model on the Husimi tree is shown. The Lyapunov exponents as new order parameters for the characterization of the model in the chaotic region are considered. The line of the continuous phase transition, which corresponds to the points of the first period doubling bifurcation, is also obtained. (C) 1998 Elsevier Science B.V.