Measuring functional renormalization group fixed-point functions for pinned manifolds

Exact numerical minimization of interface energies is used to test the functional renormalization group 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 the 1-loop calculation are compared to 2-loop corrections and chaos is measured.