Higher-order contagion processes in 3.99 dimensions

TL;DR

This paper uses a field-theoretic approach to show that higher-order interactions in contagion processes can be understood through classical physics concepts, revealing their impact on phase transitions and finite-size effects.

Contribution

It demonstrates that classical field theories can effectively describe higher-order contagion dynamics and their critical phenomena.

Findings

Pairwise mechanisms are equivalent to higher-order ones.

Coarse-grained pairwise interactions govern higher-order contact processes.

Noise and topology interplay is determined by network spectral dimension.

Abstract

Higher-order interactions have recently emerged as a promising framework for describing new dynamical phenomena in heterogeneous contagion processes. However, a fundamental open question is how to understand their contribution from the perspective of the physics of critical phenomena. Based on a mesoscopic field-theoretic Langevin description, we show that: (i) pairwise mechanisms such as facilitation or thresholding are formally equivalent to higher-order ones, (ii) pairwise interactions at coarse-grained scales govern the higher-order contact process and, (iii) the interplay between noise and topology is determined by the network spectral dimension. In short, we demonstrate that classical field theories, rooted on model symmetries and/or network dimensionality, still capture the nature of the phase transition, also predicting finite-size effects in real and synthetic networks.