Sznajd sociophysics model on a triangular lattice: ferro and antiferromagnetic opinions

Abstract

The Sznajd sociophysics model is generalized on the triangular lattice with pure antiferromagnetic opinion and also with both ferromagnetic and antiferromagnetic opinions. The slogan of the trade union "united we stand, divided we fall" can be realized via the propagation of ferromagnetic opinion of adjacent people in the union, but the propagation of antiferromagnetic opinion can be observed among the third countries between two big super powers or among the family members of conflicting parents. Fixed points are found in both models. The distributions of relaxation time of the mixed model are disperse and become loser to log-normal as the initial concentration of down spins approaches 0.5, whereas for pure antiferromagnetic spins they are collapsed into one master curve which is roughly lognormal. We do not see the phase transition in the model.