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Beyond Mean Field: Fluctuation Diagnostics and Fixed-Point Behavior

Pok Man Lo

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.

Beyond Mean Field: Fluctuation Diagnostics and Fixed-Point Behavior

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.
Paper Structure (5 sections, 54 equations, 2 figures, 1 table)

This paper contains 5 sections, 54 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Revisiting the Ginzburg-Landau criteria
  3. Kinetic Term
  4. Evolution of Fixed Points
  5. Conclusions

Figures (2)

  • Figure 1: Demonstration of the GL ratio in a linear sigma model. Top: temperature dependence at fixed explicit breaking $h$. Bottom: pseudo-critical temperature as a function of $h$. The interval $\vert T_{\rm GL}-T_c \vert$ highlights the region where MF theory is not reliable.
  • Figure 2: RG flows for several values of $u_\Lambda$. The red star marks the WFFP and the blue point the GFP. Flows run away from the GFP (fully repulsive), while the WFFP features one attractive direction, allowing trajectories to approach it.