Supersymmetry Breaking in Disordered Systems and Relation to Functional Renormalization and Replica-Symmetry Breaking

Abstract

In this article, we study an elastic manifold in quenched disorder in the limit of zero temperature. Naively it is equivalent to a free theory with elasticity in Fourier-space proportional to k^4 instead of k^2, i.e. a model without disorder in two space-dimensions less. This phenomenon, called dimensional reduction, is most elegantly obtained using supersymmetry. However, scaling arguments suggest, and functional renormalization shows that dimensional reduction breaks down beyond the Larkin length. Thus one equivalently expects a break-down of supersymmetry. Using methods of functional renormalization, we show how supersymmetry is broken. We also discuss the relation to replica-symmetry breaking, and how our formulation can be put into work to lift apparent ambiguities in standard functional renormalization group calculations.

Dedicated to Lothar Schaefer on the occasion of his 60th birthday. Revised version; some explications added

References in corpus (8)

• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Universal interface width distributions at the depinning threshold
• Higher correlations, universal distributions and finite size scaling in the field theory of depinning
• 2-loop Functional Renormalization for elastic manifolds pinned by disorder in N dimensions
• Functional renormalization group for anisotropic depinning and relation to branching processes
• Broad relaxation spectrum and the field theory of glassy dynamics for pinned elastic systems
• Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by Disorder
• Depinning transition at the upper critical dimension

Cited by in corpus (10)

• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
• Field Theories for Loop-Erased Random Walks
• Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems
• Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric ${\varphi }^4$ theory with $n\to -2$ and loop-erased random walks
• Random field and random anisotropy O(N) spin systems with a free surface
• Benchmarking the nonperturbative functional renormalization group approach on the random elastic manifold model in and out of equilibrium
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• Large Orders and Strong-Coupling Limit in Functional Renormalization