A renormalization group approach to crowd psychology and inter-group coupling in social many-body systems

By adopting majority rule within a renormalization group approach, we can show that the strength of inter-group interaction in a social system either grows or shrinks monotonically with increasing group size, depending on the initial coupling strength of individuals in the group. This contrasts with the findings of previous studies in which the strength of the interaction grows with group size regardless of the initial strength. Our approach clearly demonstrates that the phenomena of crowd psychology, such as an extreme anti-reaction between different ethnic or ideological groups, could be a consequence of the many-particle nature of social systems when the initial strength of the interaction is larger than a critical value. The effect of neutral opinion holders is critically examined using the spin-one Ising model. The critical size of the population of neutral opinion holders, that can prevent crowd polarization, depends on the block spin rule.