Characterization of the Nonequilibrium Steady State of a Heterogeneous Nonlinear q-Voter Model with Zealotry (Supplementary Material)

Supplementary material for <em>Characterization of the Nonequilibrium Steady State of a Heteogeneous Nonlinear q-Voter Model with Zealotry</em>.Authors: <em>Andrew Mellor, Mauro Mobilia, R.K.P. Zia</em><b>Items include:</b>An illustration of the model mechanism.Stationary state evolution as a function of z.Explicit expressions of LGA matrices, F and D.Vorticity and Stream Function: Definitions and Figure 3.Comparisons between precision numerical results and simulation data.Comparisons between LGA predictions and simulation results.<b>Abstract:</b>We introduce an heterogeneous nonlinear q-voter model with two types of susceptible voters and zealots, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a susceptible voter of type q₁ or q₂, or is an inflexible zealot. At each time step, a q_i-susceptible voter (i=1,2) consults a group of q_i neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. We show that this model violates the detailed balance whenever q₁≠q₂and has surprisingly rich properties. Here, we focus on the characterization of the model’s non-equilibrium stationary state (NESS) in terms of its probability distribution and currents in the distinct regimes of low and high density of zealotry. We unveil the NESS properties in each of these phases by computing the opinion distribution and the circulation of probability currents, as well as the two-point correlation functions at unequal times (formally related to a “probability angular momentum”). Our analytical calculations obtained in the realm of a linear Gaussian approximation are compared with numerical results.<b>Viewing Notes:</b>To view the supplementary materials, download all files and run index.html in a web browser (preferably Chrome).<br>