COARSENING AND PERSISTENCE IN THE VOTER MODEL

The voter model is a simple model for coarsening with a nonconserved s calar order parameter. We investigate coarsening and persistence in th e voter model by introducing the quantity P-n(t), defined as the fract ion of voters who changed their opinion n times up to time t. We show that P-n(t) exhibits scaling behavior that strongly depends on the dim ension as well as on the initial opinion concentrations. Exact results are obtained for the average number of opinion changes, [n], and the autocorrelation function, A(t)=Sigma(-1)P-n(n) similar to t(-d/2) in a rbitrary dimension d. These exact results are complemented by a mean-f ield theory, heuristic arguments, and numerical simulations. For dimen sions d>2, the system does not coarsen, and the opinion changes follow a nearly Poissonian distribution, in agreement with mean-field theory . For dimensions d less than or equal to 2, the distribution is given by a different scaling form, which is characterized by nontrivial scal ing exponents. For unequal opinion concentrations, an unusual situatio n occurs where different scaling functions correspond to the majority and the minority, as well as for even and odd n.