The recent study of large data sets has revealed the key network structures behind many biological, social, and technological processes. These structures influence how rumours and epidemics spread, the efficiency of biochemical reaction pathways, or the robustness of the air transport system. In recent years, network scientists have turned to statistical physics to help build a quantitative understanding of such systems. They’ve also realised that most networks do not exist in isolation, but are stitched together into larger interdependent systems. Such coupling means that failure of one node – a communication link, for example – can lead to a cascade of other effects in other linked networks, such as power outages and canceled flights.
In new research, LML fellow Fernando Metz and collaborators employ tools from statistical physics to study the collective behaviour of interdependent networks in a particularly simple case, using a classic model from physics: the Ising model. In this class of models, each node of the network takes on a binary value reflecting some variable – an opinion on some binary decision or choice, for example. In many models of opinion dynamics, the system eventually evolves to a consensus, all individuals having the same opinion. For coupled Ising systems, however, the authors find that two coupled networks may instead become “trapped” in a state of persisting polarisation, where two groups have opposite opinions or states, even though the influences acting between individuals favour consensus. Interestingly, the average time for escape from such a polarised state is exponentially large, which suggests that two social groups can coexist with opposite opinions for remarkably long times.
The paper is available at http://iopscience.iop.org/article/10.1088/1742-5468/aad6c7/pdf