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Published on: July 11, 2025
Crossover from the parity-conserving pair contact process with diffusion to other universality classes.
1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany.
Summary
The pair contact process with diffusion (PCPD2) shares critical behaviors with PCPD. Crossover exponents suggest PCPD has a distinct universality class from directed percolation (DP), with new routes identified.
Area of Science:
- Statistical physics
- Complex systems
Background:
- Reaction-diffusion processes are fundamental to modeling complex systems.
- Understanding universality classes and crossovers is key to classifying system behaviors.
Purpose of the Study:
- Investigate the pair contact process with diffusion with modulo 2 conservation (PCPD2).
- Analyze crossovers between PCPD2, directed Ising (DI), and directed percolation (DP) universality classes.
- Determine if PCPD belongs to a distinct universality class.
Main Methods:
- Simulations of one-dimensional reaction-diffusion systems.
- Analysis of critical behaviors and crossover exponents.
- Introduction of specific reaction terms (e.g., A-->3A) and symmetry-breaking fields.
Main Results:
- PCPD2 exhibits critical behaviors similar to PCPD.
- Identified crossover exponents (1/φ₁=0.57(3) and 1/φ₂=0.73(4)) for PCPD2-to-DI and DP-to-DI transitions.
- A new crossover route from PCPD2 to DP was found with exponent 1/φ₃=1.23(10).
Conclusions:
- The pair contact process with diffusion (PCPD) likely represents a universality class distinct from directed percolation (DP).
- The findings provide evidence for independent routes and fixed points in reaction-diffusion systems.
- This work contributes to a deeper understanding of universality and phase transitions in complex systems.
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