Hysteresis in the zero-temperature random field Ising model on directed random graphs

We use zero-temperature Glauber dynamics to study hysteresis in the random-field Ising model on directed random graphs. The critical behavior of the model depends on the connectivity $z$ of the graph rather differently from that on undirected graphs. Directed graphs and zero-temperature dynamics are relevant to a wide class of social phenomena including opinion dynamics. We discuss the efficacy of increasing external influence in inducing a first-order phase transition in opinion dynamics. The numerical results are supported by an analytic solution of the model.