Statistical physics in a three-state extended voter model

This thesis aims to give a detailed study of a set of three-state interacting particle systems that are generalizations of the conventional voter model. The proposed model, which we have called “The Extended Voter Model”, allow particles to interact following two kinds of reactions: voter reactions (where a particle adopts the state of the particle with which it has interacted), and non-voter reactions (where a particle adopts a new state different from the state of the particle with which it has interacted). Introducing this addition to the conventional voter model gives rise to several possibilities of interacting particle systems with new consensus dynamics, different from the linear behaviour for the conventional voter model. The final goal of the thesis is to understand the mechanisms that produce these new behaviours as well as to find methods to infer the consensus dynamics without the use of numerical methods.