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  • Open Access

Universality of noise-induced transitions in nonlinear voter models

Jaume Llabrés*, Maxi San Miguel, and Raúl Toral

  • *Contact author: jaumellabres@ifisc.uib-csic.es
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Phys. Rev. Research 8, 013015 – Published 9 January, 2026

DOI: https://doi.org/10.1103/6xdk-2cjy

Abstract

We analyze the universality classes of phase transitions in a variety of nonlinear voter models. By mapping several models with symmetric absorbing states onto a canonical model introduced in previous studies, we confirm that they exhibit a Generalized Voter transition. We then propose a canonical mean-field model that extends the original formulation by incorporating a noise term that eliminates the absorbing states. This generalization gives rise to a phase diagram featuring two distinct types of phase transitions: a continuous Ising transition and a discontinuous transition we call Modified Generalized Voter. These two transition lines converge at a tricritical point. We map diverse noisy nonlinear voter models onto this extended canonical form. Using finite-size scaling techniques above and below the upper-critical dimension, we show that the continuous transition of these models belongs to the Ising universality class in their respective dimensionality. We also find universal behavior at the tricritical point. Our results provide a unifying framework for classifying phase transitions in stochastic models of opinion dynamics with both nonlinearity and noise.

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Phys. Rev. Research 8, 013015– Published 9 January, 2026
  • Received 11 June 2025
  • Accepted 31 October 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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