Simulation consensus model of never changed opinions in Sznajd consensus model using multi-spin coding

TL;DR

This paper investigates the decay of never changed opinions in the Sznajd consensus model, revealing dimension-dependent exponents and the effects of different updating schemes, supported by multi-spin coding simulations.

Contribution

It introduces a detailed analysis of opinion persistence in the Sznajd model, comparing sequential and simultaneous updates, and relates findings to Ising model results.

Findings

Decay exponent theta ~= 3/8 in 1D chain

Exponent differs from Ising in higher dimensions

Simultaneous updating leads to exponential decay

Abstract

The density of never changed opinions during the Sznajd consensus-finding process decays with time t as 1/t^{theta}. We find theta ~= 3/8 for a chain, compatible with the exact Ising result of Derrida et al. In higher dimensions, however, the exponent differs from the Ising theta. With simultaneous updating of sublattices instead of the usual random sequential updating, the number of persistent opinions decays roughly exponentially. Some of the simulations used multi-spin coding.