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arXiv · 1912.08192

First-Passage Percolation under extreme disorder: from bond-percolation to Kardar-Parisi-Zhang universality

Daniel Villarrubia·Iván Álvarez Domenech·Silvia N. Santalla·Javier Rodríguez-Laguna·Pedro Córdoba-Torres
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Abstract

We consider the statistical properties of arrival times and balls on first-passage percolation (FPP) $2D$ square lattices with strong disorder in the link-times. A previous work showed a crossover in the weak disorder regime, between Gaussian and Kardar-Parisi-Zhang (KPZ) universality, with the crossover length decreasing as the noise amplitude grows. On the other hand, this work presents a very different behavior in the strong-disorder regime. A new crossover length appears below which the model is described by bond-percolation universality class. This characteristic length scale grows with the noise amplitude and diverges at the infinite-disorder limit. We provide a thorough characterization of the bond-percolation phase, reproducing its associated critical exponents through a careful scaling analysis of the balls. This is carried out through to a continuous mapping of the FPP passage time into the occupation probability of the bond-percolation problem. Moreover, the crossover length can be explained merely in terms of properties of the link-time distribution. The interplay between the new characteristic length and the correlation length intrinsic to bond-percolation determines the crossover between the initial percolation-like growth and theasymptotic KPZ scaling.

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Daniel Villarrubia, Iván Álvarez Domenech, Silvia N. Santalla, Javier Rodríguez-Laguna, Pedro Córdoba-Torres. 2019-12-17. First-Passage Percolation under extreme disorder: from bond-percolation to Kardar-Parisi-Zhang universality. https://doi.org/10.1103/physreve.101.062124

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