title: Mean-field analysis of phase transitions in the emergence of hierarchical society.
abstract: Emergence of hierarchical society is analyzed by use of a simple agent-based model. We extend the mean-field model of Bonabeau et al. [Physica A 217, 373 (1995)] to societies obeying complex diffusion rules where each individual selects a moving direction following their power rankings. We apply this mean-field analysis to the pacifist society model recently investigated by use of Monte Carlo simulation [Physica A 367, 435 (2006)]. We show analytically that the self-organization of hierarchies occurs in two steps as the individual density is increased and there are three phases: one egalitarian and two hierarchical states. We also highlight that the transition from the egalitarian phase to the first hierarchical phase is a continuous change in the order parameter and the second transition causes a discontinuous jump in the order parameter.
authors.affiliation: Department of Physics, Kyushu University, Fukuoka 812-8581, Japan. t.okubo@cmt.phys.kyushu-u.ac.jp
authors.forename: Tsuyoshi
authors.initials: T
authors.lastname: Okubo
authors.forename: Takashi
authors.initials: T
authors.lastname: Odagaki