The Renormalization Group for Disordered Systems

Abstract

In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on hierarchical lattices, which are the simplest non-mean-field systems where the RG framework emerges in a natural way. The resulting critical properties shed light on the critical behavior of spin and structural glasses beyond mean field, and suggest future directions for understanding the criticality of more realistic glassy systems.

Castellana, M. (2014). The renormalization group for disordered systems. Rome: Sapienza Universita Editrice

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• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2$ spin dynamics for Wigner and Wishart ensembles
• Self-Supervised Learning of Generative Spin-Glasses with Normalizing Flows
• The Hierarchical Parity Model