Sznajd opinion dynamics with global and local neighbourhood

TL;DR

This paper introduces a modified Sznajd opinion model on a square lattice where distant agreeing individuals influence their neighbors, revealing exponential consensus times, size-independent advertising effects, and complex multi-opinion dynamics.

Contribution

It presents a novel modification of the Sznajd model incorporating global influence and analyzes its effects on consensus formation and phase transitions.

Findings

Consensus times are exponentially distributed and small.

The phase transition width decreases inversely with lattice size.

Advertising effects are independent of system size.

Abstract

In this modification of the Sznajd consensus model on the square lattice, two people of arbitrary distance who agree in their opinions convince their nearest neighbours of this opinion. Similarly to the mean field theory of Slanina and Lavicka, the times needed to reach consensus are distributed exponentially and are quite small. The width of the phase transition vanishes reciprocally to the linear lattice dimension. Advertising has effects independent of the system size. For more than two opinions, three opinions reach a consensus in roughly half of the samples, and four only rarely and only for small lattices.