Field Theory of Disordered Elastic Interfaces at 3-Loop Order: Critical Exponents and Scaling Functions

Abstract

For disordered elastic manifolds in the ground state (equilibrium) we obtain the critical exponents for the roughness and the correction-to-scaling up to 3-loop order, i.e. third order in $\epsilon =4-d$, where $d$ is the internal dimension $d$. We also give the full 2-point function up to order ${\epsilon }^2$, i.e. at 2-loop order.

arXiv commentv1: 74 pages, 88 figures; v2: paper split into to parts; v3: typos corrected and hyper-ref enabled

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• Depinning transition of charge-density waves: mapping onto $O(n)$ symmetric ${\varphi }^4$ theory with $n\to -2$ and loop-erased random walks
• Field Theory of Disordered Elastic Interfaces at 3-Loop Order: The $\beta$-Function
• Experimental test of Sinai's model in DNA unzipping
• Benchmarking the nonperturbative functional renormalization group approach on the random elastic manifold model in and out of equilibrium
• Roughness and critical force for depinning at 3-loop order
• Large Orders and Strong-Coupling Limit in Functional Renormalization