Phase Transitions in Paradigm Shift Models

Two general models for paradigm shifts, deterministic propagation model (DM) and stochastic propagation model (SM), are proposed to describe paradigm shifts and the adoption of new technological levels. By defining the order parameter [Image: see text] based on the diversity of ideas, [Image: see text], it is studied when and how the phase transition or the disappearance of a dominant paradigm occurs as a cost [Image: see text] in DM or an innovation probability [Image: see text] in SM increases. In addition, we also investigate how the propagation processes affect the transition nature. From analytical calculations and numerical simulations [Image: see text] is shown to satisfy the scaling relation [Image: see text] for DM with the number of agents [Image: see text]. In contrast, [Image: see text] in SM scales as [Image: see text].