Opinion formation models with extreme switches and disorder: critical behaviour 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 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 $p=\frac{1-q}{4}$ where the order parameter vanishes with a universal value of the exponent $\beta =1/2$. 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 behaviour 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 behaviour remains mean field like, the system behaves more like a two state model as $q\to 1$. At $q=1$ the model behaves like a binary voter model with random flipping occurring with probability $p$.

arXiv comment7 pages, 7 figures

References in corpus (19)

• Statistical physics of social dynamics
• Freezing and Slow Evolution in a Constrained Opinion Dynamics Model
• Ordering dynamics with two non-excluding options: Bilingualism in language competition
• Disorder induced phase transition in kinetic models of opinion dynamics
• Ultimate Fate of Constrained Voters
• Role of conviction in nonequilibrium models of opinion formation
• Opinion dynamics in a three-choice system
• Consensus and ordering in language dynamics
• Mean field solutions of kinetic exchange opinion models
• Disorder induced phase transition in an opinion dynamics model: results in 2 and 3 dimensions
• The drastic outcomes from voting alliances in three-party bottom-up democratic voting (1990 $\to$ 2013)
• Phase transition in kinetic exchange opinion models with independence
• Fixation and Polarization in a Three-Species Opinion Dynamics Model
• Algebraic coarsening in voter models with intermediate states
• Boundary effects in a three-state modified voter model for languages
• Critical noise can make the minority candidate win: The US Presidential Election cases
• Long route to consensus: Two stage coarsening in a binary choice voting model
• Block size dependence of coarse graining in discrete opinion dynamics model: Application to the US presidential elections
• Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches

Cited by in corpus (1)

• Virtual walks and phase transitions in two dimensional BChS model with extreme switches