Invariant percolation properties in random isotropic systems of conductive discorectangles on a plane: From disks to sticks

Recently, some eccentricity-invariant properties of random, isotropic, two-dimensional (2D) systems of conductive ellipses have been reported [Phys. Rev. B \bf{104}, 184205 (2021)]. Moreover, the authors suggested that this invariance might also be observed in systems with other particle geometries having zero-width sticks as the limiting case. To check this suggestion, we studied 2D random systems of isotropically-placed, overlapping, identical discorectangles (stadia) with aspect ratios ranging from 1 (disks) to $\infty$ (zero-width sticks). We analyzed the effect of the aspect ratio and the number density of conductive discorectangles on the behavior of the electrical conductivity, the local conductivity exponent, and the current-carrying backbone. Our own computer simulations demonstrate that some of the properties of random, isotropic 2D systems of conductive discorectangles are insensitive to the aspect ratios of the particles.
8 pages, 13 figures, 32 references