Screening of Deeply Invaginated Clusters and the Critical Behavior of the Random Superconducting Network

Antonio Coniglio; H. Eugene Stanley

doi:10.1103/PhysRevLett.52.1068

Screening of Deeply Invaginated Clusters and the Critical Behavior of the Random Superconducting Network

Antonio Coniglio and H. Eugene Stanley

Phys. Rev. Lett. 52, 1068 – Published 26 March 1984

Abstract

Starting with an expression for the fractal dimension $d_{u}$ of the unscreened perimeter of an arbitrary fractal of dimension $d_{f}$ , there are derived for the random superconducting network the results $\tilde{s} = (2 - d) + d_{u}$ , from which follow ${\tilde{ϕ}}_{s} = d_{u}$ and $d_{w} = d - d_{u}$ . Here $\tilde{s}$ is the conductivity exponent, ${\tilde{ϕ}}_{s}$ the conductance exponent, and $d_{w}$ the fractal dimension of a random walk on the network. For $d = 2$ , these results differ from the Alexander-Orbach conjecture by 0.3%.