A stochastic opinion dynamics model with domain size dependent dynamic evolution

Abstract

We introduce a stochastic model of binary opinion dynamics in one dimension. The binary opinions $\pm 1$ are analogous to up and down Ising spins and in the equivalent spin system, only the spins at the domain boundary can flip. The probability that a spin at the boundary is up is taken as $P_{up}=\frac{s_{up}}{s_{up}+\delta s_{down}}$ where $s_{up}(s_{down})$ denotes the size of the domain with up (down) spins neighbouring it. With $x$ fraction of up spins initially, a phase transition is observed in terms of the exit probability and the phase boundary is obtained in the $\delta -x$ plane. In addition, we investigate the coarsening behaviour starting from a completely random state; conventional scaling is observed only at the phase transition point $\delta =1$. The scaling behaviour is compared to other dynamical phenomena; the model apparently belongs to a new dynamical universility class as far as persistence is concerned although the dynamical exponent, equal to one, is identical to a similar model with no stochasticity.

This paper has been withdrawn by the authors. An updated, revised and accepted version (in PRE) of this paper is available at arXiv:1306.6813

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• Universal features of exit probability in opinion dynamics models with domain size dependent dynamics
• Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches
• Minority spin dynamics in non-homogeneous Ising model: diverging timescales and exponents
• Impact of Preference and Equivocators on Opinion Dynamics with Evolutionary Game Framework
• Non-equilibrium dynamics in Ising like models with biased initial condition