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arXiv · 1808.08099

Perturbing the Shortest Path on a Critical Directed Square Lattice

Fabian Hillebrand·Mirko Luković·Hans J. Herrmann
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Abstract

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 $α= 1.36 \pm 0.01$ for the path length differences and $β= 1.186 \pm 0.001$ for the enclosed areas.

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Fabian Hillebrand, Mirko Luković, Hans J. Herrmann. 2018-08-24. Perturbing the Shortest Path on a Critical Directed Square Lattice. https://doi.org/10.1103/physreve.98.052143

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