Optimal path cracks in correlated and uncorrelated lattices

Details Optimal path cracks in correlated and uncorrelated lattices Optimal path cracks in correlated and uncorrelated lattices

2011-01-31

arxiv.org/abs/1101.5910v1

Phys. Rev. E 83, 046113 (2011)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 10 figures

Scientific paper

10.1103/PhysRevE.83.046113

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 beta/nu = 0.46 \pm 0.03 we report, for the first time, gamma/nu = 1.3 \pm 0.2 and tau = 2.3 \pm 0.2. The analysis is extended to surfaces with spatial long-range power-law correlations, where non-universal 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 \pm 0.05.

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