Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines

Abstract

We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions. We disclose that these models have numerically equivalent fractal dimensions and leading correction-to-scaling exponents. We conjecture all three models to possess the same fractal dimension, namely, $d_f=1.2168\pm 0.0005$ in 2D and $d_f=2.487\pm 0.003$ in 3D, and the same exponent of the leading correction, $\Omega =0.9\pm 0.1$ and $\Omega =1.0\pm 0.1$, respectively. The close relations between watersheds, optimal path cracks in the strong disorder limit, and bridge lines are further supported by either heuristic or exact arguments.

References in corpus (4)

• Explosive percolation via control of the largest cluster
• Correction-to-scaling exponent for two-dimensional percolation
• New efficient methods to calculate watersheds
• Impact of Perturbations on Watersheds

Cited by in corpus (3)

• Watersheds are Schramm-Loewner Evolution curves
• Stacked triangular lattice: Percolation properties
• How to share underground reservoirs