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By Fereydoon Family, Mohamed Daoud, Hans J. Herrmann, H. Eugene Stanley
Foreign Workshop and choice of articles honoring Professor Antonio Coniglio at the party of his sixtieth birthday. convention held April 13-14, 2000 in Paris, France. meant for experts in addition to graduate and postdoctoral scholars operating in condensed-matter or statistical physics.
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Rausch. We also acknowledge support from the German-Israeli Foundation. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982). C. M. Fortuin and P. W. Kasteleyn, Physica (Utrecht) 57, 536 (1972). T. Grossman and A. Aharony, J. Phys. A19, L745 (1986); 20, L1193 (1987). A. Coniglio, J. Phys. A15, 3829 (1982). A. Coniglio, Phys. Rev. Lett. 62, 3054 (1989). H. Saleur and B. Duplantier, Phys. Rev. Lett. 58, 2325 (1987). M. Aizenman, B. Duplantier and A. Aharony, Phys.
De Arcangelis, A. Coniglio and S. Redner, Phys. Rev. B36, 5631 (1987). 10. H. Herrmann and S. ), Statistical Models for the Fracture of Disordered Media (NorthHolland, 1990). 11. P. Grassberger, Physica A262, 251 (1999). 12. Y. Lee, J . S. Andrade J r , S. V. Buldyrev, S. Havlin, P. R. King, G. Paul and H. E. Stanley, prepn'nt Cond-Mat 9903066. 13. M. Barthklkmy, S. V. Buldyrev, S. Havlin and H. E. Stanley, Phys. Rev. E60, R1123 (1999). 14. H. J. Herrmann, D. Hong and H. E. Stanley, J. Phys. A17, L261 (1984).
In a second part, we study the multifractal spectrum of the current in the twodimensional random resistor network at the percolation threshold. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small i as P ( i ) N l / i where i is the current. As a consequence, the moments of i of order q 5 q, = 0 diverge with system size, and all sets of bonds with current values below the most probable one have the fractal dimension of the backbone. Hence we hypothesize that the backbone can be described in terms of only (i) blobs of fractal dimension d B and (ii) high current carrying bonds of fractal dimension going from dred to d B , where dred is the fractal dimension of the red bonds carrying the maximal current.