Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods

Details Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods

1994-02-04

arxiv.org/abs/cond-mat/9402019v1

Physics

Condensed Matter

19 pages, LaTeX, 5 figures uuencoded, BONN HE-94-02

Scientific paper

10.1007/BF02180139

The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\rightarrow A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial conditions as well. Two different numerical methods are used to compute the scaling properties: Monte Carlo simulations and extrapolations of exact finite lattice data. These methods are tested in a case where analytical results are available. It is shown that Monte Carlo simulations can be used to compute even the correction terms. To obtain reliable results from finite-size extrapolations exact numerical data for lattices up to ten sites are sufficient.

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