Comment on "Dynamic opinion model and invasion percolation".

In [1], Shao et al. claim, based on low statistics simulations , that a model with majority rule coarsening exhibits in d ¼ 2 a percolation transition in the universality class of invasion percolation with trapping (IPT). They report also that the system reaches its final state rapidly with no diverging time scale. Since the original configurations are random and thus in the ordinary percolation (OP) univer-sality class, it seems unlikely that long range correlations could develop in a finite time that would change this. Indeed, it was proved rigorously [2] that similar 2D models (called ''dependent percolation'' in [2]) belong to the OP universality class. Here, we present high statistics (up to L ¼ 2 14 , >10 4 realizations) on L Â L square lattices and confirm that the phase transition is in the OP universality class, thus refuting a central tenet of [1]. Initially, each site i is randomly assigned one of two opinions (or spins): i ¼ þ1, with probability f; otherwise, i ¼ À1. At each time step, all sites are updated in parallel. If at least three of their four neighbors disagree with them, they change their opinion; otherwise, they keep it. As noted in [1], this leads quickly [within Oð10Þ time steps] to a static state, except for sites that flip permanently with period 2. The critical probability f c where a ''þ1'' cluster percolates depends slightly on how these flicker sites are treated (we treat them as ''þ,'' if i ¼ þ1 at even times), but the universal properties do not. We first determine f c by measuring the chance that a cluster in the final state percolates through lattices with open boundary conditions. Using finite size scaling [3], we obtain f c ¼ 0:506 425ð20Þ, in agreement with the less precise estimate of [1]. After that, we measure the distribution of cluster sizes with ¼ þ1 in final states obtained with helical boundary conditions for f % f c. Figure 1 confirms the above estimate of f c and shows that the data are excellently described by a power law PðsÞ $ s À with the OP critical exponent ¼ 187=91 % 2:055, ruling out the IPT exponent % 1:89. We see also deviations from this power law at small masses s, as small clusters are eliminated by the coarsening. This, together with using open boundary conditions and neglecting finite size …