B P Lee 1994 J. Phys. A: Math. Gen. 27 2633 doi:10.1088/0305-4470/27/8/004
B P Lee
Show affiliationsThe diffusion-controlled reaction kA to OE is known to be strongly dependent on fluctuations in dimensions d<or=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.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
82C28 Dynamic renormalization group methods (See also 81T17)
82C21 Dynamic continuum models (systems of particles, etc.)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
Issue 8 (21 April 1994)
B P Lee 1994 J. Phys. A: Math. Gen. 27 2633
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