Phase of Ising spins on modular networks analogous to social polarization

TL;DR

This paper studies how Ising spins on modular networks exhibit two-stage ordering, revealing that societal polarization can persist even when interactions favor consensus, due to the network's modular structure.

Contribution

It introduces a model analyzing phase transitions in modular networks, showing the emergence of persistent polarization at different temperature thresholds.

Findings

Local ordering occurs at a critical temperature within modules.

Global ordering happens at a lower temperature across the entire network.

Polarization can persist indefinitely despite interactions favoring consensus.

Abstract

Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks, corresponding to consensus formation in society, we observe two distinct phases: (i) ordering within each module at a critical temperature, followed by (ii) global ordering at a lower temperature. This indicates polarization of society into groups having contrary opinions can persist indefinitely even when mutual interactions between agents favor consensus.