Based on an equivalence between the q-state Potts model and conformally invariant field theories, the author speculates that all fractal dimensionalities of two-dimensional percolation are given by the formula D=(100-x2)/48, where x is an integer. The same formula should also apply to self-avoiding walks and lattice animals. This approach is extended to cluster-weighted percolation. His conjecture seems to agree with previous exact and numerical results except for the backbone exponent, and possibly for lattice animals.
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T. A. Larsson (1987) studied this question.
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