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  • Open Access

Phase transitions for polyadic epidemic and voter models with multiscale groups

Pia Steinmeyer1,*, Jan Mölter1,*, and Christian Kuehn1,2,3

  • *These authors contributed equally to this work.
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Phys. Rev. E 112, 044305 – Published 10 October, 2025

DOI: https://doi.org/10.1103/jcj3-pwrj

Abstract

Polyadic (or higher-order) interactions can significantly impact the dynamics of interacting particle systems. However, previous studies have often assumed group sizes to be relatively small. In this work, we examine the influence of multiscale polyadic group interactions, where some groups are small and others are very large. We consider two paradigmatic examples, an SIS-epidemic and the adaptive voter model. On the level of the mean field, we specifically discuss the impact of the multiscale polyadic interactions on equilibrium dynamics and phase transitions. For the SIS-epidemic model, we find a region of bistability that protects the disease-free state over a wide range beyond the classical epidemic threshold from a significant outbreak. For the adaptive voter model, we show that multiscale polyadic interactions can stabilize the network or increase the convergence rate to an unbiased equilibrium.

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Phys. Rev. E 112, 044305– Published 10 October, 2025
  • Received 16 October 2024
  • Revised 18 July 2025
  • Accepted 8 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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