Equilibrium and nonequilibrium in the three-dimensional Q2R cellular automata

Area of Science:

• Complex Systems
• Statistical Physics
• Computational Science

Background:

• Cellular automata (CA) are discrete dynamical systems modeling complex phenomena.
• The Q2R (Quantum 2R) model is a conservative and reversible CA with a large state space.
• Understanding CA dynamics is crucial for modeling physical systems.

Purpose of the Study:

• To investigate the equilibrium and nonequilibrium dynamics of the Q2R cellular automata.
• To analyze the phase space, identify fixed points and cycles, and observe system behaviors.
• To explore the impact of a coupling constant perturbation on the Q2R model's phase diagram.

Main Methods:

• Numerical simulations were employed to study the system dynamics.
• A statistical approach was utilized for analyzing system behavior.
• Phase diagrams were generated to visualize the effects of the coupling constant.

Main Results:

• The Q2R model exhibits fixed points and cycles in its phase space for small system sizes.
• A critical energy (E_c) was identified, around which a phase transition occurs.
• The modified Q2R model with a coupling constant displays three distinct phases.

Conclusions:

• The Q2R cellular automata demonstrates complex dynamics, including stable and unstable behaviors.
• A phase transition is a key feature of the Q2R model, influenced by energy levels.
• Perturbing the Q2R model with a coupling constant leads to a richer phase structure with multiple distinct phases.