title: Exact solution of the nonconsensus opinion model on the line.
abstract: The nonconsensus 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 possible 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.
authors: Physics Department, Clarkson University, Potsdam, New York 13699-5820, USA. benavraham@clarkson.edu
authors: Daniel
authors: D
authors: ben-Avraham