Universal persistence exponent in transition to antiferromagnetic order in coupled logistic maps

Area of Science:

• Complex Systems
• Statistical Physics
• Nonlinear Dynamics

Background:

• Coupled logistic maps model complex behaviors in dynamical systems.
• Understanding phase transitions and critical phenomena is crucial in statistical physics.

Purpose of the Study:

• To investigate the dynamics and phase transitions of coupled logistic maps on a 1D lattice.
• To analyze the persistence properties and critical exponents of the system.

Main Methods:

• Coarse-graining the logistic map system by labeling local states (+ or -).
• Analyzing transitions between global states, including moving defects and time-frozen states.
• Investigating long-range antiferromagnetic order and power-law behavior of persistence P(t).

Main Results:

• Observed a transition from a dynamic state with moving defects to a frozen state (modulo-2).
• Identified a state with long-range antiferromagnetic order at the critical line.
• Found a universal persistence exponent of 3/8 for synchronous dynamics, deviating from the expected 3/4.

Conclusions:

• The system exhibits distinct phase transitions with implications for understanding complex dynamics.
• The universal persistence exponent suggests a deep connection between different dynamical systems.
• A plausible argument for the observed scaling of the persistence exponent is presented.