Branching and annihilating Levy flights

Details Branching and annihilating Levy flights Branching and annihilating Levy flights

2000-11-28

arxiv.org/abs/cond-mat/0011475v1

Phys. Rev. E 63, 041116 (2001).

Physics

Condensed Matter

Statistical Mechanics

9 pages, 4 figures

Scientific paper

10.1103/PhysRevE.63.041116

We consider a system of particles undergoing the branching and annihilating reactions A -> (m+1)A and A + A -> 0, with m even. The particles move via long-range Levy flights, where the probability of moving a distance r decays as r^{-d-sigma}. We analyze this system of branching and annihilating Levy flights (BALF) using field theoretic renormalization group techniques close to the upper critical dimension d_c=sigma, with sigma<2. These results are then compared with Monte-Carlo simulations in d=1. For sigma close to unity in d=1, the critical point for the transition from an absorbing to an active phase occurs at zero branching. However, for sigma bigger than about 3/2 in d=1, the critical branching rate moves smoothly away from zero with increasing sigma, and the transition lies in a different universality class, inaccessible to controlled perturbative expansions. We measure the exponents in both universality classes and examine their behavior as a function of sigma.

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