Percolation in a kinetic opinion exchange model (1110.6819v2)

Abstract: We study the percolation transition of the geometrical clusters in the square lattice LCCC model (a kinetic opinion exchange model introduced by Lallouache et al. in Phys. Rev. E 82 056112 (2010)) with the change in conviction and influencing parameter. The cluster comprises of the adjacent sites having an opinion value greater than or equal to a prefixed threshold value of opinion (\Omega). The transition point is different from that obtained for the transition of the order parameter (average opinion value) found by Lallouache et al. Although the transition point varies with the change in the threshold value of the opinion, the critical exponents for the percolation transition obtained from the data collapses of the maximum cluster size, cluster size distribution and Binder cumulant remain same. The exponents are also independent of the values of conviction and influencing parameters indicating the robustness of this transition. The exponents do not match with that of any other known percolation exponents (e.g. the static Ising, dynamic Ising, standard percolation) and thus characterizes the LCCC model to belong to a separate universality class.