Opinion formation models with extreme switches and disorder: Critical behavior and dynamics.

Abstract

In a three-state kinetic exchange opinion formation model, the effect of extreme switches was considered in a recent paper. In the present work, we study the same model with disorder. Here disorder implies that negative interactions may occur with a probability p. In the absence of extreme switches, the known critical point is at p_{c}=1/4 in the mean-field model. With a nonzero value of q that denotes the probability of such switches, the critical point is found to occur at p=1-q/4 where the order parameter vanishes with a universal value of the exponent β=1/2. Stability analysis of initially ordered states near the phase boundary reveals the exponential growth (decay) of the order parameter in the ordered (disordered) phase with a timescale diverging with exponent 1. The fully ordered state also relaxes exponentially to its equilibrium value with a similar behavior of the associated timescale. Exactly at the critical points, the order parameter shows a power-law decay with time with exponent 1/2. Although the critical behavior remains mean-field-like, the system behaves more like a two-state model as q→1. At q=1 the model behaves like a binary voter model with random flipping occurring with probability p.