title: Optimal-path cracks in correlated and uncorrelated lattices.
abstract: 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.
authors: Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970 Fortaleza, Ceará, Brazil. erneson@fisica.ufc.br
authors: E A
authors: EA
authors: Oliveira
authors: K J
authors: KJ
authors: Schrenk
authors: N A M
authors: NA
authors: Araújo
authors: H J
authors: HJ
authors: Herrmann
authors: J S
authors: JS
authors: Andrade