  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.
