Phase transitions in a two parameter model of opinion dynamics with random kinetic exchanges

TL;DR

This paper extends a kinetic exchange opinion model by introducing two parameters, revealing a phase transition characterized by a phase boundary, with critical behavior and non-universal exponents, and analyzing the dynamics near the transition.

Contribution

The model is generalized to include conviction and influence parameters, deriving a phase boundary and analyzing critical behavior and non-universality in opinion dynamics.

Findings

Identified a phase boundary at λ=1−μ/2 separating phases.

Observed power-law divergence of time scales near the transition.

Found non-universal critical exponents along the phase boundary.

Abstract

Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry breaking transition was reported [M. Lallouache et al, Phys. Rev. E, {\bf 82} 056112 (2010)]. We generalise the model to incorporate two parameters, $\lambda$, to represent conviction and $\mu$, to represent the influencing ability of individuals. A phase boundary given by $\lambda=1-\mu/2$ is obtained separating the symmetric and symmetry broken phases: the effect of the influencing term enhances the possibility of reaching a consensus in the society. The time scale diverges near the phase boundary in a power law manner. The order parameter and the condensate also show power law growth close to the phase boundary albeit with different exponents. Theexponents in general change along the phase boundary indicating a non-universality. The relaxation times, however, become constant with increasing system size near the phase boundary indicating the absence of any diverging length scale. Consistently, the fluctuations remain finite but show strong dependence on the trajectory along which it is estimated.