Phase transition classes in triplet and quadruplet reaction-diffusion models

Area of Science:

• Statistical Physics
• Complex Systems
• Chemical Kinetics

Background:

• Reaction-diffusion systems are fundamental to understanding pattern formation and emergent behavior.
• Site occupation restrictions and multi-particle reactions introduce complex dynamics not captured by simple models.

Purpose of the Study:

• Investigate phase transitions in low-dimensional reaction-diffusion systems with specific particle creation and diffusion rules.
• Analyze models with nA-->(n+k)A and mA-->(m-l)A reaction types.
• Compare simulation results with mean-field approximations and existing literature.

Main Methods:

• Mean-field approximation applied to lattice models.
• Extensive computer simulations in one and two dimensions.
• Analysis of critical behavior and phase transition types.

Main Results:

• The 3A-->4A, 3A-->2A model shows a continuous mean-field phase transition in d=2, with a critical dimension d(c)<2.
• In d=1, this model exhibits mean-field behavior with logarithmic corrections, contradicting prior studies.
• The 4A-->5A, 4A-->3A model displays mean-field behavior with logarithmic corrections in d=2, and nontrivial transitions in d=1, suggesting d(c)=2.
• A parity conserving model (3A-->5A, 2A-->0) in d=1 shows a continuous phase transition with unique exponents.

Conclusions:

• The study reveals diverse critical behaviors in reaction-diffusion systems, deviating from predictions of phenomenological Langevin equations.
• Mean-field theory provides a valuable framework, but logarithmic corrections and non-trivial transitions highlight system-specific complexities.
• Discrepancies with prior work underscore the importance of detailed simulation and analytical approaches for specific reaction-diffusion models.