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

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Branching annihilating random walks with long-range attraction exhibit critical behavior dependent on bias strength. A threshold at σ=1 separates directed Ising universality class behavior from non-DI behavior.

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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.