Abstract
A method for studying the exact properties of a class of inhomogeneous stochastic many-body systems is developed and presented in the framework of a voter model perturbed by the presence of a “zealot,” an individual allowed to favor an “opinion.” We compute exactly the magnetization of this model and find that in one (1D) and two dimensions (2D) it evolves, algebraically () in 1D and much slower () in 2D, towards the unanimity state chosen by the zealot. In higher dimensions the stationary magnetization is no longer uniform: the zealot cannot influence all the individuals. The implications to other physical problems are also pointed out.
- Received 6 February 2003
DOI:https://doi.org/10.1103/PhysRevLett.91.028701
©2003 American Physical Society