Phase transitions in Paradigm models

TL;DR

This paper introduces two models for paradigm shifts, analyzing how ideas evolve and transition in social systems through analytical and numerical methods, highlighting the effects of costs and innovation probabilities.

Contribution

It proposes deterministic and stochastic models for paradigm shifts and derives scaling relations for the order parameter based on system parameters.

Findings

The order parameter scales with system size and parameters in both models.

Analytical calculations match numerical simulations.

Transition behavior depends on cost and innovation probability.

Abstract

In this letter we propose two general models for paradigm shift, deterministic propagation model (DM) and stochastic propagation model (SM). By defining the order parameter $m$ based on the diversity of ideas, $\Delta$, we study when and how the transition occurs as a cost $C$ in DM or an innovation probability $\alpha$ in SM increases. In addition, we also investigate how the propagation processes affect on the transition nature. From the analytical calculations and numerical simulations $m$ is shown to satisfy the scaling relation $m=1-f(C/N)$ for DM with the number of agents $N$. In contrast, $m$ in SM scales as $m=1-f(\alpha^a N)$.