Abstract. The diffusion-controlled reaction kA to OE is known to be strongly dependent on fluctuations in dimensions d<or=d_c=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 =d_c-d. For the density it is found that, asymptotically, n approximately A_kt^-d2/. The decay exponent is exact to all orders in epsilon , and the amplitude A_k 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=d_c we find n approximately A_k(In t/t)^1(k-1) with an exact expression for A_k. 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.

Print publication: Issue 8 (21 April 1994)