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arXiv · 1301.4751

Phase transitions in Paradigm models

Huiseung Chae·Soon-Hyung Yook·Yup Kim
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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, $Δ$, we study when and how the transition occurs as a cost $C$ in DM or an innovation probability $α$ 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 $m=1-f(α^a N)$.

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Huiseung Chae, Soon-Hyung Yook, Yup Kim. 2013-01-21. Phase transitions in Paradigm models. https://doi.org/10.1371/journal.pone.0070928

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