Phase of Ising spins on modular networks analogous to social polarization

Subinay Dasgupta, Raj Kumar Pan, Sitabhra Sinha

Published 2009-03-26, updated 2009-08-08Version 2

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.