Monte Carlo fixed scale transformation for nonlocal fractal growth models

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.