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Discrete scale invariance in supercritical percolation.

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Schröder,  Malte
Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Nagler,  Jan
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Schröder, M., Chen, W., & Nagler, J. (2016). Discrete scale invariance in supercritical percolation. New Journal of Physics, 18(1): 013042. doi:10.1088/1367-2630/18/1/013042.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-D59E-C
Abstract
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order parameter (Chen et al 2014 Phys. Rev. Lett. 112 155701). Here we report the discovery of macrotransition cascades which follow percolation. The order parameter grows in discrete macroscopic steps with positions that can be randomly distributed even in the thermodynamic limit. These transition positions are, however, correlated and follow scaling laws which arise from discrete scale invariance (DSI) and non self-averaging, both traditionally unrelated to percolation. We reveal the DSI in ensemble measurements of these non self-averaging systems by rescaling of the individual realizations before averaging.