Nonuniversality in the pair contact process with diffusion

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• The one-dimensional pair contact process with diffusion is a model for systems with local interactions and spatial spread.
• Understanding its phase transitions and critical behavior is crucial for various fields, including population dynamics and material science.

Purpose of the Study:

• To investigate the static and dynamic properties of the 1D pair contact process with diffusion.
• To analyze the influence of diffusion rate on critical exponents and system behavior.
• To understand the anomalous scaling of the order-parameter moment ratio.

Main Methods:

• Analysis of static and dynamic behavior.
• Investigation of critical exponents and their dependence on diffusion rate.
• Examination of the order-parameter probability density and its scaling properties.
• Focus on distinct diffusive and reactive sectors within the active phase.

Main Results:

• Critical exponents were found to vary with the diffusion rate.
• The order-parameter moment ratio exhibits logarithmic growth with system size.
• Anomalous behavior of the order-parameter moment ratio is attributed to a violation of scaling in the order parameter probability density.
• Precise estimates for exponents beta and nu(perpendicular) were obtained for the reactive sector, confirming finite size scaling.

Conclusions:

• The presence of two distinct sectors (diffusive and reactive) explains the anomalous behavior observed.
• The study determined m(c)=1.334 for the parity-conserving universality class in one dimension.
• Finite size scaling is confirmed within the reactive sector.