Long-range interactions in Sznajd consensus model

TL;DR

This paper investigates how long-range interactions affect the phase transition behavior in the Sznajd opinion spreading model and its simplification, revealing that long-range influences can induce phase transitions.

Contribution

It introduces a modification to the Sznajd model with distance-dependent convincing strength and analyzes its impact on phase transitions, including a mixed-rule variant.

Findings

Phase transition occurs in the full Sznajd model with long-range interactions.

No phase transition in the Ochrombel simplification with long-range interactions.

Mixing the two rules favors the occurrence of a phase transition.

Abstract

The traditional Sznajd model, as well as its Ochrombel simplification, for opinion spreading are modified to have a convincing strength proportional to a negative power of the spatial distance. We find the usual phase transition in the full Sznajd model, but not in the Ochrombel simplification. We also mix the two rules, which favours a phase transition.