Zusammenfassung
The elastic backbone is the set of all shortest paths. We found a new
phase transition at p(eb) above the classical percolation threshold at
which the elastic backbone becomes dense. At this transition in 2D, its
fractal dimension is 1.750 +/- 0.003, and one obtains a novel set of critical exponents beta(eb) = 0.50 +/- 0.02, gamma(eb) = 1.97 +/- 0.05, and nu(eb) = 2.00 +/- 0.02, fulfilling consistent critical scaling laws.
Interestingly, however, the hyperscaling relation is violated. Using
Binder's cumulant, we determine, with high precision, the critical
probabilities p(eb) for the triangular and tilted square lattice for
site and bond percolation. This transition describes a sudden
rigidification as a function of density when stretching a damaged
tissue.
Nutzer