Revisiting the non-equilibrium phase transitions of the continuous-trait Axelrod model
Abstract
We investigate the non-equilibrium phase transitions of the continuous-trait Axelrod model, an agent-based framework where individual culture is represented by a vector of F continuous features confined to the interval (0,1). Local interactions are governed by a metric similarity threshold d, which acts as a continuous control parameter of social tolerance. The dynamics inevitably freeze into one of two absorbing configuration classes: an ordered, homogeneous monocultural state at high tolerance, or a highly fragmented, disordered state at low tolerance. While previous studies characterized the transition as hybrid based on the continuous behavior of the domain density μ alongside a discontinuous jump in the largest domain fraction ρ, we show that this apparent continuity is an artifact of severe finite-size masking effects. By shifting the methodological focus to the scaling of the median μ̃ and analyzing the full probability distributions P(μ), we unveil a clear bimodal structure with disjoint maxima across independent simulation runs. Our results reveal that for F=2, the system undergoes a genuinely hybrid transition in the contemporary sense, featuring a tiny but finite latent jump (μc ≈ 0.089) at the critical threshold dc ≈ 0.0784 while scaling toward it from below via a non-analytical power law with a mean-field exponent β≈ 1/2. Conversely, for F=3, the higher trait-space dimensionality suppresses local fluctuations, yielding a traditional, non-hybrid first-order transition. We apply this framework to the alternative discrete Poisson variant of the model, successfully confirming its known continuous transition for F=2 and discontinuous, non-hybrid transition for F=3, thereby establishing a unified characterization of phase transitions in Axelrod-like systems.
Versions
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BibTeX
@misc{reia2026revisiting,
title = {{Revisiting the non-equilibrium phase transitions of the continuous-trait Axelrod model}},
author = {Sandro M. Reia and Paulo R. A. Campos and José F. Fontanari},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.10381},
eprint = {2607.10381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.10381},
}
RIS
TY - UNPB
TI - Revisiting the non-equilibrium phase transitions of the continuous-trait Axelrod model
AU - Sandro M. Reia
AU - Paulo R. A. Campos
AU - José F. Fontanari
PY - 2026
DA - 2026/08/25
PB - arXiv
DO - 10.48550/arxiv.2607.10381
UR - https://arxiv.org/abs/2607.10381
AB - We investigate the non-equilibrium phase transitions of the continuous-trait Axelrod model, an agent-based framework where individual culture is represented by a vector of F continuous features confined to the interval (0,1). Local interactions are governed by a metric similarity threshold d, which acts as a continuous control parameter of social tolerance. The dynamics inevitably freeze into one of two absorbing configuration classes: an ordered, homogeneous monocultural state at high tolerance, or a highly fragmented, disordered state at low tolerance. While previous studies characterized the transition as hybrid based on the continuous behavior of the domain density μ alongside a discontinuous jump in the largest domain fraction ρ, we show that this apparent continuity is an artifact of severe finite-size masking effects. By shifting the methodological focus to the scaling of the median μ̃ and analyzing the full probability distributions P(μ), we unveil a clear bimodal structure with disjoint maxima across independent simulation runs. Our results reveal that for F=2, the system undergoes a genuinely hybrid transition in the contemporary sense, featuring a tiny but finite latent jump (μ_c ≈ 0.089) at the critical threshold d_c ≈ 0.0784 while scaling toward it from below via a non-analytical power law with a mean-field exponent β≈ 1/2. Conversely, for F=3, the higher trait-space dimensionality suppresses local fluctuations, yielding a traditional, non-hybrid first-order transition. We apply this framework to the alternative discrete Poisson variant of the model, successfully confirming its known continuous transition for F=2 and discontinuous, non-hybrid transition for F=3, thereby establishing a unified characterization of phase transitions in Axelrod-like systems.
ER -