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arXiv · 1912.09420

Erd\"os-R\'enyi phase transition in the Axelrod model on complete graphs

Sebastián Pinto·Pablo Balenzuela
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Abstract

The Axelrod model has been widely studied since its proposal for social influence and cultural dissemination. In particular, the community of statistical physics focused on the presence of a phase transition as a function of its two main parameters, $F$ and $Q$. In this work, we show that the Axelrod model undergoes a second order phase transition in the limit of $F \rightarrow \infty $ on a complete graph. This transition is equivalent to the Erd\"os-R\'enyi phase transition in random networks when it is described in terms of the probability of interaction at the initial state, which depends on a scaling relation between $F$ and $Q$. We also found that this probability plays a key role in sparse topologies by collapsing the transition curves for different values of the parameter $F$.

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Sebastián Pinto, Pablo Balenzuela. 2019-12-19. Erd\"os-R\'enyi phase transition in the Axelrod model on complete graphs. https://doi.org/10.1103/physreve.101.052319

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