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Perturbing the Shortest Path on a Critical Directed Square Lattice

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 نشر من قبل Mirko Lukovic
 تاريخ النشر 2018
  مجال البحث فيزياء
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We investigate the behaviour of the shortest path on a directed two-dimensional square lattice for bond percolation at the critical probability $p_c$ . We observe that flipping an edge lying on the shortest path has a non-local effect in the form of power-law distributions for both the differences in shortest path lengths and for the minimal enclosed areas. Using maximum likelihood estimation and extrapolation we find the exponents $alpha = 1.36 pm 0.01$ for the path length differences and $beta = 1.186 pm 0.001$ for the enclosed areas.



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