Scaling and fractal formation in persistence
- 23 March 2000
- journal article
- letter
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 33 (12) , L109-L114
- https://doi.org/10.1088/0305-4470/33/12/103
Abstract
The spatial distribution of unvisited/persistent sites in 1D A +A Ø model is studied numerically. Over length scales smaller than a cut-off (t )~tz , the set of unvisited sites is found to be a fractal. The fractal dimension df , dynamical exponent z and persistence exponent are related through z (1-df ) = . The observed values of df and z are found to be sensitive to the initial density of particles. We argue that this may be due to the existence of two competing length scales, and discuss the possibility of a crossover at late times.Keywords
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