Sznajd opinion dynamics with global and local neighbourhood

In this modification of the Sznajd consensus model on the square lattice, two people of arbitrary distance who agree in their opinions convince their nearest neighbours of this opinion. Similarly to the mean field theory of Slanina and Lavicka, the times needed to reach consensus are distributed exponentially and are quite small. The width of the phase transition vanishes reciprocally to the linear lattice dimension. Advertising has effects independent of the system size. For more than two opinions, three opinions reach a consensus in roughly half of the samples, and four only rarely and only for small lattices.