Multicomponent binary spreading process

Area of Science:

• Statistical Physics
• Complex Systems
• Mathematical Modeling

Background:

• Binary spreading processes are fundamental models for diffusion and reaction dynamics.
• Generalizations involving multiple components and interaction types introduce complex emergent behaviors.
• Understanding phase transitions in these systems is crucial for predicting macroscopic outcomes from microscopic rules.

Purpose of the Study:

• To numerically explore phase transitions in two-component generalizations of binary spreading processes.
• To analyze models with competing processes: pair annihilation, diffusion, and binary pair production.
• To classify phase transitions based on their universality classes and critical exponents.

Main Methods:

• Numerical simulations of one-dimensional spreading models.
• Investigation of various spatial production mechanisms.
• Analysis of order parameter exponents to identify universality classes.

Main Results:

• A phase transition at zero production rate (sigma=0) was identified for models with 2A --> 3A, 2B --> 3B and 2A --> 2AB, 2B --> 2BA production rules.
• This transition belongs to the N-component asymmetric branching and annihilating random walks universality class, with beta=2.
• A different model (AB --> ABA, BA --> BAB) exhibited a phase transition at sigma(c)=0.3253, characteristic of one-component binary spreading processes.

Conclusions:

• The study reveals distinct phase transition behaviors in generalized binary spreading models based on production rules.
• The classification of these transitions into known universality classes provides insights into their fundamental nature.
• These findings contribute to the understanding of complex systems dynamics and critical phenomena.