Mobilia, M.
Does a single zealot affect an infinite group of voters?
Physical Review Letters
10.1103/PhysRevLett.91.028701
91
2
028701
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<sup>-1/2</sup>) 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
lattice theory;
magnetisation;
N-body problems;
spin systems;
statistical mechanics;
stochastic systems;
APS
2003