Effects of mass media on opinion spreading in the Sznajd sociophysics model

TL;DR

This study investigates how mass media influence affects opinion dynamics in the Sznajd sociophysics model, revealing a critical media influence level that alters phase transition behavior and impacts relaxation times.

Contribution

It introduces a probabilistic external media influence into the Sznajd model and analyzes its effects on phase transitions and relaxation dynamics through Monte Carlo simulations.

Findings

Critical media influence p~0.18 suppresses phase transition.

Higher p decreases average relaxation times τ.

Relaxation times follow a power-law dependence on lattice size.

Abstract

In this work we consider the influence of mass media in the dynamics of the two-dimensional Sznajd model. This influence acts as an external field, and it is introduced in the model by means of a probability $p$ of the agents to follow the media opinion. We performed Monte Carlo simulations on square lattices with different sizes, and our numerical results suggest a change on the critical behavior of the model, with the absence of the usual phase transition for $p>\sim 0.18$. Another effect of the probability $p$ is to decrease the average relaxation times $\tau$, that are log-normally distributed, as in the standard model. In addition, the $\tau$ values depend on the lattice size $L$ in a power-law form, $\tau\sim L^{\alpha}$, where the power-law exponent depends on the probability $p$.