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Branching and annihilating Lévy flights
1Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6.
Summary
This study explores particle systems with branching and annihilation, revealing how Lévy flight behavior shifts critical transition points. Different particle movement patterns lead to distinct universality classes in absorbing-active phase transitions.
Area of Science:
- Statistical Physics
- Non-equilibrium Systems
- Complex Systems
Background:
- Investigates particle systems with simultaneous branching (A-->(m+1)A) and annihilation (A+A-->Ø) reactions.
- Incorporates long-range Lévy flights, where movement probability decays as r^(-d-sigma).
Purpose of the Study:
- To analyze branching and annihilating Lévy flight systems using field theoretic renormalization group (RG) techniques.
- To compare RG results with Monte Carlo simulations in one dimension (d=1).
- To understand the impact of the Lévy flight parameter sigma on critical behavior and universality classes.
Main Methods:
- Field theoretic renormalization group (RG) analysis near the upper critical dimension (d(c)=sigma).
- Monte Carlo simulations in d=1.
- Measurement of critical exponents as a function of sigma.
Main Results:
- For sigma near 1 in d=1, the absorbing-active phase transition occurs at zero branching rate.
- For sigma > 3/2 in d=1, the critical branching rate increases with sigma, indicating a different universality class.
- This second universality class is inaccessible via controlled perturbative expansions.
Conclusions:
- The system exhibits distinct critical behaviors depending on the Lévy flight parameter sigma.
- A transition between universality classes occurs around sigma ≈ 3/2 in d=1.
- RG and simulations provide complementary insights into these complex non-equilibrium phenomena.