How to measure the effective action for disordered systems

TL;DR

This paper reviews recent advances in measuring the non-analytic effective action in disordered systems using the Functional Renormalization Group, bridging theory, simulations, and experiments.

Contribution

It introduces methods to measure the non-analytic effective action in disordered systems, highlighting progress beyond traditional dimensional reduction predictions.

Findings

Non-analytic effective actions can be measured in simulations and experiments.

The Functional Renormalization Group captures the complex disorder landscape.

Recent numerical work supports the theoretical framework.

Abstract

In contrast to standard critical phenomena, disordered systems need to be treated via the Functional Renormalization Group. The latter leads to a coarse grained disorder landscape, which after a finite renormalization becomes non-analytic, thus overcoming the predictions of the seemingly exact dimensional reduction. We review recent progress on how the non-analytic effective action can be measured both in simulations and experiments, and confront theory with numerical work.