Branching annihilating random walks with long-range attraction in one dimension

Area of Science:

• Statistical Physics
• Complex Systems
• Stochastic Processes

Background:

• Branching annihilating random walks (BAWL) are models of particle systems with birth and death processes.
• Long-range interactions can significantly alter the collective behavior of such systems.
• Understanding phase transitions and critical exponents is crucial in statistical physics.

Purpose of the Study:

• To introduce and investigate a novel model: branching annihilating random walks with long-range attraction (BAWL).
• To determine the influence of the long-range attraction's strength (σ) on the system's critical behavior.
• To identify the universality class of the observed phase transitions.

Main Methods:

• Extensive Monte Carlo simulations were employed to study the BAWL model.
• The critical decay exponent (δ) was analyzed as a function of the bias strength parameter σ.
• The behavior of particle density in the absorbing phase was investigated.

Main Results:

• The critical decay exponent δ varies continuously with σ for σ < 1.
• For σ ≥ 1, the critical decay exponent δ matches that of the directed Ising (DI) universality class.
• The threshold σ=1 was identified as the point separating DI and non-DI critical behavior.

Conclusions:

• The strength of long-range attraction (σ) critically influences the universality class of branching annihilating random walks.
• The directed Ising universality class governs the system's behavior for strong enough attraction (σ ≥ 1).
• Branching bias with symmetric hopping shares critical behavior with BAWL, suggesting robustness of the findings.