Renormalization-group derivation for heterogeneous networks in social contagion

Derive a full Renormalization-Group treatment for information-propagation criticality on heterogeneous social networks that accounts for the observed universal cascade-size scaling and permits principled classification of universality classes in online spreading.

Background

Evidence of critical behavior and universality in social contagion has been observed across platforms, with cascade-size distributions collapsing onto a universal s^{-3/2} scaling after appropriate rescaling. These findings, obtained by coupling a Random Field Ising Model with Belief Propagation and validated on Telegram, Twitter, and Weibo datasets, strongly suggest a common universality class.

Despite this empirical and modeling support, a rigorous Renormalization-Group (RG) derivation that explains these observations for heterogeneous networks is still missing. Such a derivation would ground the observed critical exponents, clarify the role of network heterogeneity and semantic-field disorder, and systematize universality-class identification for online information spreading.