Exact solution of the Nonconsensus Opinion Model on the line

Abstract

The nonconcensus opinion model (NCO) introduced recently by Shao et al., [Phys. Rev. Lett.103, 018701 (2009)] is solved exactly on the line. Although, as expected, the model exhibits no phase transition in one dimension, its study is interesting because of the connection with invasion percolation with trapping. The system evolves exponentially fast to the steady-state, rapidly developing long-range correlations: The average cluster size in the steady state scales as the square of the initial cluster size, of the (uncorrelated) initial state. We also discuss briefly the NCO model on Bethe lattices, arguing that its phase transition diagram is different than that of regular percolation.

New version corrects some spurious mistakes, conforms with version to be published (PRE - Rapid Communication)

References in corpus (2)

• Percolation on hyperbolic lattices
• Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees

Cited by in corpus (6)

• Non-consensus opinion models on complex networks
• Homophily on social networks changes evolutionary advantage in competitive information diffusion
• Non-consensus opinion model on directed networks
• A dynamical model for competing opinions
• Autonomous models on a Cayley tree
• Growing spin model in deterministic and stochastic trees