Physics Graduate Student Symposium

Our next session is August 14th, 2025 at 12:00 PM

Renormalization of Complex Networks

Connie Sheeran

First Year, Department of Physics

A longstanding challenge in statistical physics and complex systems is extending renormalization group (RG) methods beyond regular lattices to the richly heterogeneous topologies of real-world networks. Traditional RG techniques rely on translational invariance and uniform coarse-graining, leaving critical questions about phase transitions, universality, and multiscale dynamics in (e.g. neural) networks unanswered. This talk introduces a unified, exact real-space RG framework for the Ising model on arbitrary graphs, bridging the gap between microscopic interactions and emergent macroscopic behavior. Monte Carlo simulations validate the derived flow equations on one-dimensional chains, Bethe lattices, random regular graphs and Erdős-Rényi graphs. The resulting toolkit establishes a foundation for discovering novel universality classes and for controlling dynamical processes on complex networks. Future work is also presented.

Click here for a full list of PGSS 2025 Speakers