Exact solution of the Nonconsensus Opinion Model on the line

Details Exact solution of the Nonconsensus Opinion Model on the line Exact solution of the Nonconsensus Opinion Model on the line

2011-01-18

arxiv.org/abs/1101.3447v2

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

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.

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