Abstract
We investigate coarsening and persistence in the voter model by introducing the quantity Pn (t),
defined as the fraction of voters who changed their opinion n times up to time t. We show that
Pn (t) exhibits scaling behavior that strongly depends on the dimension 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) ≡ (−1)n Pn ∼ t−d/2 in arbitrary dimension d. These exact
results are complemented by a mean-field theory, heuristic arguments and numerical simulations. For
dimensions 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 ≤ 2, the distribution is given
by a different scaling form, which is characterized by nontrivial scaling exponents. For unequal
opinion concentrations, an unusual situation occurs where different scaling functions correspond to
the majority and the minority, as well as for even and odd n.
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