Abstract
We consider reaction-diffusion systems of a single species (A + A → φ) in the absence and the presence of a particle input. Applying renormalization group theory to a field theoretic description and matching theory to the renormalization group trajectory integrals of the systems, we find that for d < 2 in the absence of an input, the density decays as c(t) ∼ t-ν with the dynamic exponent ν = d/2 and in the presence of input the density grows as c(I) ∼ Iμ with the static exponent μ = d/(d + 2), while for d > 2 the behaviors are mean-field like and for d = 2 there are logarithmic corrections to the mean-field results. The results for the absence of input are consistent with the previous results obtained using different methods. In addition, we propose a rigorous proof of Racz's conjecture about the relation between the static and the dynamic exponents, μ = ν/(1 + ν).
Original language | English |
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Pages (from-to) | L6-L8 |
Journal | Journal of the Korean Physical Society |
Volume | 34 |
Issue number | 1 |
State | Published - 1999 |