Measuring functional renormalization group fixed-point functions for pinned manifolds

TL;DR

This paper uses numerical minimization to test the functional renormalization group analysis for pinned interfaces, confirming key features like the cusp in the fixed-point function R(u) across various disorder types and dimensions.

Contribution

It provides the first numerical verification of the FRG fixed-point function R(u) and explores deviations from 1-loop predictions, including 2-loop corrections and chaos cross-correlations.

Findings

Confirmed the linear cusp in R''(u) for multiple disorder types and dimensions.

Observed deviations from 1-loop FRG results, consistent with 2-loop corrections.

Compared cross-correlations with FRG predictions for chaos phenomena.

Abstract

Exact numerical minimization of interface energies is used to test the functional renormalization group (FRG) analysis for interfaces pinned by quenched disorder. The fixed-point function R(u) (the correlator of the coarse-grained disorder) is computed. In dimensions D=d+1, a linear cusp in R''(u) is confirmed for random bond (d=1,2,3), random field (d=0,2,3), and periodic (d=2,3) disorders. The functional shocks that lead to this cusp are seen. Small, but significant, deviations from 1-loop FRG results are compared to 2-loop corrections. The cross-correlation for two copies of disorder is compared with a recent FRG study of chaos.