Critical behavior of the one-dimensional diffusive pair contact process

Area of Science:

• Statistical Physics
• Complex Systems Dynamics
• Phase Transitions

Background:

• The diffusive pair contact process is a model for systems with particle creation, annihilation, and diffusion.
• Understanding its phase transitions, particularly in one dimension, is crucial for statistical physics.
• Previous studies on the one-dimensional diffusive pair contact process yielded conflicting results regarding its transition behavior.

Purpose of the Study:

• To investigate the phase transition of the one-dimensional diffusive pair contact process.
• To compare results from N cluster mean-field approximations with high-precision simulations.
• To clarify the order parameter exponents and their dependence on diffusion rate (D).

Main Methods:

• Utilized N cluster mean-field approximations (N=3, 4).
• Performed high-precision dynamical simulations on large lattices (L=10^5).
• Analyzed order parameter exponents and applied finite-size scaling techniques.

Main Results:

• N=3, 4 cluster approximations predict a smooth transition line, differing from N=2 results.
• Simulation data for 0.05 <= D <= 0.7 may support distinct transition classes.
• A single class behavior with logarithmic corrections (alpha=0.21(1), beta=0.40(1)) is a plausible interpretation of the numerical data.

Conclusions:

• Higher-order mean-field approximations suggest a unified transition behavior.
• Simulation results present a complex picture, potentially reconcilable with a single universality class under specific conditions.
• The study highlights the importance of simulation precision and theoretical refinements in understanding complex system dynamics.