The Chaotic Properties of the Q-state Potts Model on the Bethe Lattice:Q<2
N.S. Ananikian, S.K. Dallakian, B. Hu
TL;DR
This paper explores the chaotic dynamics of the Q-state Potts model on the Bethe lattice for Q<2, revealing complex bifurcation behavior and phase transitions through Lyapunov exponents and thermodynamic formalism.
Contribution
It introduces a detailed analysis of chaos and phase transitions in the Potts model for Q<2 using Lyapunov exponents and dynamical systems techniques.
Findings
Magnetization exhibits bifurcation and chaos.
Distribution of Lyapunov exponents shows scaling behavior.
Identifies phase transition points via chaotic free energy.
Abstract
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''.
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Taxonomy
TopicsTheoretical and Computational Physics · Quantum chaos and dynamical systems · Quantum many-body systems