Abstract (may include machine translation)
In this paper we address the question of the existence of a well defined, non-trivial fractal dimension D of self-affine clusters. In spite of the obvious relevance of such clusters to a wide range of phenomena, this problem is still open since the different published predictions for D have not been tested yet. An interesting aspect of the problem is that a nontrivial global dimension for clusters is in contrast with the trivial global dimension of self-affine functions. As a much studied example of self-affine structures, we investigate the infinite directed percolation cluster at the threshold. We measured D in d=2 dimensions by the box counting method. Using a correction to scaling analysis, we obtained D=1.765(10). This result does not agree with any of the proposed relations, but it favors D=1+(1-σν∥)/σν⊥, where ν∥ and ν⊥ are the correlation length exponents and σ is a Fisher exponent in the cluster scaling.
Original language | English |
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Pages (from-to) | 829-841 |
Number of pages | 13 |
Journal | Journal of Statistical Physics |
Volume | 64 |
Issue number | 3-4 |
DOIs | |
State | Published - Aug 1991 |
Externally published | Yes |
Keywords
- Fractal dimension
- directed percolation
- self-affinity