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Measuring functional renormalization group fixed-point functions for pinned manifolds

A. Alan Middleton·Pierre Le Doussal·Kay Joerg Wiese
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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.

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A. Alan Middleton, Pierre Le Doussal, Kay Joerg Wiese. 2006-06-07. Measuring functional renormalization group fixed-point functions for pinned manifolds. https://doi.org/10.1103/physrevlett.98.155701

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