Optimal-path cracks in correlated and uncorrelated lattices.

The optimal path crack model on uncorrelated surfaces, recently introduced by Andrade et al. [Phys. Rev. Lett. 103, 225503 (2009).], is studied in detail and its main percolation exponents computed. In addition to β/ν=0.46±0.03, we report γ/ν=1.3±0.2 and τ=2.3±0.2. The analysis is extended to surfaces with spatial long-range power-law correlations, where nonuniversal fractal dimensions are obtained when the degree of correlation is varied. The model is also considered on a three-dimensional lattice, where the main crack is found to be a surface with a fractal dimension of 2.46±0.05.