Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branching and annihilating Levy flights   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.

12
The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
1
The categories of this paper are: cs