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We compute the Functional Renormalization Group (FRG) disorder- correlatorfunction R(v) for d-dimensional elastic manifolds pinned by a random potentialin the limit of infinite embedding space dimension N. It measures theequilibrium response of the manifold in a quadratic potential well as thecenter of the well is varied from 0 to v. We find two distinct scaling regimes:(i) a "single shock" regime, v^2 ~ 1/L^d where L^d is the system volume and(ii) a "thermodynamic" regime, v^2 ~ N. In regime (i) all the equivalentreplica symmetry breaking (RSB) saddle points within the Gaussian variationalapproximation contribute, while in regime (ii) the effect of RSB enters onlythrough a single anomaly. When the RSB is continuous (e.g., for short-rangedisorder, in dimension 2 <= d <= 4), we prove that regime (ii) yields thelarge-N FRG function obtained previously. In that case, the disorder correlatorexhibits a cusp in both regimes, though with different amplitudes and ofdifferent physical origin. When the RSB solution is 1-step and non- marginal(e.g., d < 2 for SR disorder), the correlator R(v) in regime (ii) isconsiderably reduced, and exhibits no cusp. Solutions of the FRG flowcorresponding to non-equilibrium states are discussed as well. In all cases theregime (i) exhibits a cusp non-analyticity at T=0, whose form and thermalrounding at finite T is obtained exactly and interpreted in terms of shocks.The results are compared with previous work, and consequences for manifolds atfinite N, as well as extensions to spin glasses and related models arediscussed.

physical review. b, condensed matter and materials physics

Cusps and shocks in the renormalized potential of glassy random  manifolds: How Functional Renormalization Group and Replica Symmetry Breaking  fit together