Renormalization group calculation for the reaction kA to OE

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Abstract
The diffusion-controlled reaction kA to OE is known to be strongly dependent on fluctuations in dimensions dc=2/(k-1). We develop a field-theoretic renormalization group approach to this system which allows explicit calculation of the observables as expansions in epsilon 1(k-1), where epsilon =dc-d. For the density it is found that, asymptotically, n approximately Akt-d2/. The decay exponent is exact to all orders in epsilon , and the amplitude Ak is universal, and is calculated to second order in epsilon 1(k-1) for k=2, 3. The correlation function is calculated to first order, along with a long-wavelength expansion for the second-order term. For d=dc we find n approximately Ak(In t/t)1(k-1) with an exact expression for Ak. The formalism can be immediately generalized to the reaction kA to LA, L<k, with the consequence that the density exponent is the same, but the amplitude is modified.
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