Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-02-28
J. Phys. A: Math. Gen. 38 (2005) 8187-8199
Physics
Condensed Matter
Statistical Mechanics
(v1,2) 8 pages, 5 figures; one-loop calculation corrected in response to criticism received from Hans-Karl Janssen, (v3) conte
Scientific paper
10.1088/0305-4470/38/38/001
We derive a generic expression for the generating function (GF) of the particle-number probability distribution (PNPD) for a simple reaction diffusion model that belongs to the directed percolation universality class. Starting with a single particle on a lattice, we show that the GF of the PNPD can be written as an infinite series of cumulants taken at zero momentum. This series can be summed up into a complete form at the level of a mean-field approximation. Using the renormalization group techniques, we determine logarithmic corrections for the GF at the upper critical dimension. We also find the critical scaling form for the PNPD and check its universality numerically in one dimension. The critical scaling function is found to be universal up to two non-universal metric factors.
Anton Lucian
Park Hyunggyu
Park Su-Chan
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