Non-monotonic spontaneous magnetization in a Sznajd-like Consensus Model

TL;DR

This paper studies a Sznajd-like consensus model showing that adding optimal noise can enhance societal consensus, with the system exhibiting non-monotonic magnetization behavior due to stable opinion islands.

Contribution

It demonstrates that in a synchronous Sznajd model, a finite amount of noise maximizes overall consensus, revealing non-monotonic magnetization dynamics.

Findings

Maximum consensus occurs at finite noise levels.

Stable opinion islands are disrupted by noise, increasing overall agreement.

System exhibits non-monotonic orientation with respect to noise.

Abstract

Ising or Potts models of ferromagnetism have been widely used to describe locally interacting social or economic systems. We consider a related model, introduced by Sznajd to describe the evolution of consensus in a society. In this model, the opinion or state of any spins can only be changed through the influence of neighbouring pairs of similarly aligned spins. Such pairs can polarize their neighbours. We show that, assuming the global dynamics evolve in a synchronous manner, the two-state Sznajd model exhibits a non-monotonically decreasing overall orientation that has a maximum value when the system is subject to a finite value of noise. Reinterpreting the model in terms of opinions within a society we predict that consensus can be increased by the addition of an appropriate amount of random noise. These features are explained by the presence of islands of complete orientation that are stable in the absence of noise but removed via the presence of added noise.