Finite-scale singularity in the renormalization group flow of a reaction-diffusion system

Area of Science:

• Statistical Physics
• Complex Systems
• Condensed Matter Physics

Background:

• The pair contact process with diffusion (PCPD) is a model for studying nonequilibrium phase transitions.
• Understanding the critical behavior of such systems is crucial for various fields, including statistical physics and material science.
• Standard perturbation theory often struggles with complex, interacting systems far from equilibrium.

Purpose of the Study:

• To investigate the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD).
• To explore the limitations of standard perturbation theory in describing PCPD.
• To identify the universality classes governing PCPD critical phenomena.

Main Methods:

• Nonperturbative functional renormalization group (FRG) techniques were employed.
• The study analyzed the effective potential and its nonanalyticities.
• The research involved incorporating dynamically generated terms to continue the renormalization group flow.

Main Results:

• Standard perturbation theory was found to fail for PCPD due to nonanalyticity in the effective potential at a finite length scale.
• Dynamically generated terms, forbidden by perturbation theory, were identified and incorporated.
• The renormalization group flow was successfully continued by accounting for these generated terms.

Conclusions:

• The critical behavior of PCPD is not accurately captured by standard perturbation theory.
• The findings suggest that PCPD critical behavior can fall into the directed percolation universality class.
• Alternatively, PCPD critical behavior might belong to a different, conjugated universality class, highlighting novel critical phenomena.