Abstract
The fixed scale transformation (FST) is a theoretical framework developed for the evaluation of scaling dimensions in a vast class of complex systems showing fractal geometric correlations. For models with long range interactions, such as Laplacian growth models, the identification by analytical methods of the transformation's basic elements is a very difficult task. Here we present a Monte Carlo renormalization approach which allows the direct numerical evaluation of the FST transfer matrix, overcoming the usual problems of analytical and numerical treatments. The scheme is explicitly applied to the diffusion limited aggregation case where a scale invariant regime is identified and the fractal dimension is computed. The Monte Carlo FST represents an alternative tool which can be easily generalized to other fractal growth models with nonlocal interactions.
Keywords
fixed-scale transformation (FST)
Subject Categories
Fractals, Monte Carlo method, Renormalization (Physics)
Disciplines
Physics
Publisher
American Physical Society
Publication Date
1-1-1997
Rights Information
©1997 American Physical Society
Rights Holder
American Physical Society
Permanent URL
Recommended Citation
Piccioni, M; Cafiero, R; and Vespignani, A, "Monte Carlo fixed scale transformation for nonlocal fractal growth models" (1997). Physics Faculty Publications. Paper 219. http://hdl.handle.net/2047/d20002179
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Notes
Originally published in Physical Review E, v.55 no.1 (1997), pp.1170-1173. DOI:10.1103/PhysRevE.55.1170. Dr. Vespignani is affiliated with Northeastern University as of the time of deposit.