Phys. Rev. Lett. 91, 028701 (2003) [4 pages]Does a Single Zealot Affect an Infinite Group of Voters?Received 6 February 2003; revised 30 April 2003; published 11 July 2003 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 (∼t-1/2) in 1D and much slower (∼1/lnt) 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. © 2003 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.91.028701
DOI:
10.1103/PhysRevLett.91.028701
PACS:
89.75.Hc, 02.50.Le, 05.50.+q, 75.10.Hk
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