Block Voter Model

TL;DR

This paper introduces the block voter model with noise on 2D lattices, analyzing how persuasive cluster size influences phase transitions and critical behavior, revealing Ising-like universality regardless of interaction range.

Contribution

The study presents a new outflow dynamics model with persuasive clusters, exploring their impact on phase transitions and critical phenomena in opinion dynamics.

Findings

Order-disorder phase transition occurs for PCS size > 2.

Critical noise parameter increases with PCS size.

Critical behavior is Ising-like regardless of interaction range.

Abstract

We introduce and study the block voter model with noise on two-dimensional square lattices using Monte Carlo simulations and finite-size scaling techniques. The model is defined by an outflow dynamics where a central set of $N_{PCS}$ spins, here denoted by persuasive cluster spins (PCS), tries to influence the opinion of their neighbouring counterparts. We consider the collective behaviour of the entire system with varying PCS size. When $N_{PCS}>2$, the system exhibits an order-disorder phase transition at a critical noise parameter $q_{c}$ which is a monotonically increasing function of the size of the persuasive cluster. We conclude that how large the PCS is more power of persuasion it has. It also seems that the resulting critical behaviour is Ising-like independent of the range of the interactions.