Physical Manifestation of Interdependent Networks

Interdependent networks (IN) is a theoretical concept studied in network theory for over a decade. IN are composed of two networks interacting with two types of interactions, connectivity within networks and dependency between them. Recently, we manifested this paradigm in physical systems by introducing Physical Interdependent Networks (PINs). Examples of PINs are Interdependent Ferromagnetic Networks (IFN) and Interdependent Superconducting Networks (ISN), where the latter was recently validated in lab experiments. PINs are characterized by two types of interactions: Connectivity links within each network represent magnetic interactions in IFN or enable current to flow in ISN, while dependency is realized by heat dissipation between the networks. PINs show new phenomena due to the thermal interdependent interaction between the layers. While isolated superconducting and ferromagnetic networks experience a second-order phase transition, once networks interact thermally the transition becomes first-order. Furthermore, both IFN and ISN show long-living plateau behavior at the critical point similar to percolation on interdependent networks with the same critical exponents indicating a novel shared universality class of interdependent systems despite the different physical features. Our results suggest technological applications for fabricating a new class of complex interdependent materials with unique properties based on the critical phenomena observed in PINs.