Universality of noise-induced transitions in nonlinear voter models

TL;DR

This paper demonstrates that various noisy nonlinear voter models exhibit universal phase transition behavior, classifiable into Ising and tricritical universality classes, through a unified mean-field framework.

Contribution

It introduces a canonical mean-field model with noise that unifies diverse nonlinear voter models and classifies their phase transitions into known universality classes.

Findings

Continuous transitions belong to the Ising universality class.

Universal behavior observed at the tricritical point.

Phase diagram includes both continuous and discontinuous transitions.

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 (GV) 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 (MGV). 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 tricitical point. Our results provide a unifying framework for classifying phase transitions in stochastic models of opinion dynamics with both nonlinearity and noise.