Agreement dynamics on directed random graphs. (28th June 2017) - Lipowski, Adam; Lipowska, Dorota; Ferreira, António Luis
Abstract: We examine some agreement-dynamics models that are placed on directed random graphs. In such systems, a fraction of sites exp ⁡ ( − z ), where z is the average degree, become permanently fixed or flickering. In the voter model, which has no surface tension, such zealots or flickers freely spread their opinions and that makes the system disordered. For models with a surface tension, like the Ising model or the Naming Game model, their role is limited, and such systems are ordered at large z . However, when z decreases, the density of zealots or flickers increases, and below a certain threshold ( z ∼ 1.9 − 2.0 ) the system becomes disordered. On undirected random graphs, agreement dynamics is very different and ordering appears as soon the graph is above the percolation threshold at z   =  1.