Noise, ageing and multiplexity in the voter model

The voter model is a paradigmatic example of a model of opinion competition in a population of agents. Despite its name, which one could wrongly identify and reduce to another model of opinion dynamics, the model is quite general. It is solvable in any dimension in regular lattices, well studied both analytically and numerically and its dynamics (with the corresponding equations) can be equivalently mapped into other areas of research, like genetic drift problems or heterogeneous catalyses. However, the underlying rules of this dynamical model are simple. It is fair and sensible, therefore, to include realistic ingredients in the modeling, study their consequences and check if they describe or fit better the natural phenomena around.

In this talk I will discuss the phenomenology of some of these variations, namely, the noise and the ageing in the update rates of the agents and the effect of embedding the agents in multiplex topologies. Separately, each one of these elements introduces effects of different nature. On the one hand, ageing alone forces the system to reach consensus (the absorbing state of the dynamics) though a coarsening process, regardless of the dimensionality and the system size, which is totally contrary to what occurs in the standard voter model. On the other hand, noise eliminates the absorbing states of the system and induces a finite-size transition in the stationary distribution of the magnetization. When these elements combine, both in monoplexes and multilayer topologies, a plethora of emergents results arise: trapping states different than consensus, second-order phase transitions or spontaneous symmetry breaking, to name a few. I will review all of them in detail during the seminar.