Chaotic Properties of the Q-state Potts Model on the Bethe Lattice: Q < 2
N. S. Ananikian
S. K. Dallakian
Department of Physics and the Centre for Nonlinear Studies,
Hong Kong Baptist University, Hong Kong, China
and
Department of Theoretical Physics, Yerevan Physics Institute,
Alikhanian Br.2, 375036 Yerevan, Armenia
B. Hu
Department of Physics and the Centre for Nonlinear Studies,
Hong Kong Baptist University, Hong Kong, China
and
Department of Physics, University of Houston,
Houston, TX, USA
Abstract
The Q-state Potts model on the Bethe lattice is investigated for Q < 2. The magnetization of this model exhibits complicated behavior including both period doubling bifurcation and chaos. The Lyapunov exponents of the Potts-Bethe map are considered as order parameters. A scaling behavior in the distribution of Lyapunov exponents in the fully developed chaotic case is found. Using the canonical thermodynamic formalism of dynamical systems, the nonanalytic behavior in the distribution of Lyapunov exponents is investigated and the phase transition point on the "chaotic free energy" is located.
