Beyond Mean Field: Fluctuation Diagnostics and Fixed-Point Behavior

TL;DR

This paper introduces diagnostics for identifying mean-field theory breakdown, analyzing how spatial structure and interaction ranges influence effective descriptions and alter renormalization-group flow.

Contribution

It provides new theoretical tools to understand the limitations of mean-field theory and the impact of spatial and interaction scales on renormalization-group behavior.

Findings

Diagnostics reveal when mean-field theory fails.

Spatial structure modifies effective descriptions.

Interaction ranges qualitatively change RG flow.

Abstract

We develop theoretical diagnostics for the breakdown of mean-field theory, demonstrate how spatial structure and finite interaction ranges enter the effective description, and show how these scales qualitatively modify the renormalization-group flow.