2016/01/19 by Malte Schröder, Wei Chen, Jan Nagler · 1 citation
Materials Science · Physics and Astronomy · #Complex Network Analysis Techniques #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1088/1367-2630/18/1/013042
published as New Journal of Physics, 18, 013042 (2016) · 8 pages, 8 figures
openalex publication_date 2016/01/19 · arxiv created 2016/01/22 · arxiv updated 2016/01/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 macro transition 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.