Study and characterization of interfaces in a two-dimensional generalized voter model.

We propose and study, by means of numerical simulations, the time evolution of interfaces in a generalized voter model in d=2 dimensions. In this model, a randomly selected voter can change his or her opinion (state) with a certain probability that is an algebraic function of the average opinion of his or her nearest neighbors. By starting with well-defined (sharp) interfaces between two different states of opinion, we measure the time dependence of the interface width (w), which behaves as a power law, i.e., w α t(δ). In this way we characterized three different types of interfaces: (i) between an ordered phase (consensus) and a disordered one (δ=1/2); (ii) between ordered phases having different states of opinion (δ=1/2), which corresponds to interface coarsening without surface tension; and (iii) as in (ii) but considering surface tension. Here, we observe a finite-size induced crossover with exponents δ=1/4 and δ=1/2 for early and longer times, respectively. So, our study allows for the characterization of interfaces of quite different nature in a unified fashion, providing insight into the understanding of interface coarsening with and without surface tension.