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

Abstract

We have studied a walk in a one-dimensional virtual space corresponding to an extended version of the three-state BChS model of opinion formation, originally proposed in Physica A {\bf 391}, 3257 (2012), in which the agents are located on a two dimensional lattice. The opinions are designated by the values $\pm 1$ and zero. Here we also consider switches between the extreme states $\pm 1$. The model involves two noise parameters representing the fraction of negative interactions $p$ and the probability of extreme switch denoted by $q$. The study shows that the nature of the walks changes drastically as the noise parameters exceed certain threshold values. The order-disorder phase transitions are independently obtained using the finite size scaling method showing that these threshold values are indeed consistent with those values of the parameters where a phase transition exists. The criticality is found to be Ising-like even when extreme switches are allowed. A new critical exponent associated with the probability distribution of the displacement is also obtained independent of the values of the critical parameters. The nature of the walks is compared to similar virtual walks studied earlier.

arXiv comment6 pages, 10 figures

References in corpus (17)

• Statistical physics of social dynamics
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• The Emergence of Consensus: A Primer
• Disorder induced phase transition in kinetic models of opinion dynamics
• Large deviations and nontrivial exponents in coarsening systems
• Disorder induced phase transition in an opinion dynamics model: results in 2 and 3 dimensions
• Stationary definition of persistence for finite temperature phase ordering
• 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
• Agent dynamics in kinetic models of wealth exchange
• Block size dependence of coarse graining in discrete opinion dynamics model: Application to the US presidential elections
• Virtual walks inspired by a mean field kinetic exchange model of opinion dynamics
• A poor agent and subsidy: an investigation through CCM model
• Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches
• Antipersistent dynamics in kinetic models of wealth exchange
• Virtual walks in spin space: a study in a family of two-parameter models
• Opinion formation models with extreme switches and disorder: critical behaviour and dynamics