A New (aleph) Stochastic Quenched Disorder Model for Interaction of Network- Master node

Abstract: We consider a first neighbor interaction where agents are spread through a uni-dimensional network. Some agents are also connected to a hub, or master node, who has preferential values (or orientation). The role of master node is to persuade some individuals to follow a specific orientation, subject to a probability of successful persuasion. The connections between master node and the network society are quenched in disorder. Despite its simplicity, we found a phase transition from disorder to order for three different control parameters. We also discuss how this model may be useful as a framework to study the spread of morality, innovation, opinion formation and consensus. Is important to recall the route from disorder to order in social systems still a great challenge. We hope to contribute with a novel approach to model a this issues.