Critical decay exponent of the pair contact process with diffusion

Area of Science:

• Statistical Physics
• Complex Systems
• Nonlinear Dynamics

Background:

• The pair contact process with diffusion (PCPD) is a model system for studying spreading phenomena.
• Understanding critical exponents is crucial for classifying universality classes in statistical mechanics.

Purpose of the Study:

• To accurately determine the critical density decay exponent (δ) for the one-dimensional PCPD.
• To investigate the influence of diffusion rate on scaling corrections and critical behavior.
• To analyze crossover phenomena and their implications for the PCPD's universality class.

Main Methods:

• Extensive Monte Carlo simulations were employed to model the PCPD.
• A recently introduced method was used to find the strength of corrections to scaling.
• Effective exponents were systematically analyzed to determine the critical decay exponent.
• Crossover behaviors at different diffusion rates (d=0 and d=1) were studied.

Main Results:

• The leading corrections to scaling exhibit different behaviors for small (∼t^{-0.15}) and large (∼t^{-0.5}) diffusion rates.
• The critical decay exponent δ was found to be 0.173(3), independent of the diffusion rate.
• A discontinuous phase boundary was observed at d=0, with a crossover exponent ϕ=2.6(1).
• At d=1, the crossover exponent was found to be ϕ=2, suggesting an exact value.

Conclusions:

• The determined critical decay exponent (δ=0.173(3)) provides a key characteristic of the one-dimensional PCPD.
• The discontinuity at d=0 challenges the hypothesis that PCPD belongs to the directed percolation universality class.
• The crossover exponent at d=1 supports exact theoretical predictions for mean-field behavior.