2000/06/30 by Pascal Chauve, Pierre Le Doussal, Kay Jörg Wiese +1 · 218 citations
Materials Science · Mathematics · Physics and Astronomy · #Classical mechanics #Force Microscopy Techniques and Applications #Loop (graph theory) #Material Dynamics and Properties #Mathematics #Physics #Quantum electrodynamics #Quantum mechanics #Renormalization #Statistical physics #Theoretical and Computational Physics #Work (physics) #cond-mat
paper · pdf · doi:10.1103/physrevlett.86.1785
published in Physical Review Letters 86(9), 1785-1788 (American Physical Society) · Revised version, easier to read, 2 tables and comparison with experiments added
arxiv created 2000/10/20 · openalex publication_date 2001/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the field theories for pinned elastic systems at equilibrium and at depinning. Their \ensuremathβ functions differ to two loops by novel ``anomalous'' terms. At equilibrium we find a roughness \ensuremathζ\phantom\rule0ex0ex=\phantom\rule0ex0ex0.20829804\ensuremathε+0.006858\ensuremathε2 (random bond), \ensuremathζ\phantom\rule0ex0ex=\phantom\rule0ex0ex\ensuremathε/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find \ensuremathζ\phantom\rule0ex0ex=\phantom\rule0ex0ex\frac\ensuremathε3(1+0.14331\ensuremathε), \ensuremathε\phantom\rule0ex0ex=\phantom\rule0ex0ex4\ensuremath-d, in violation of the conjecture \ensuremathζ\phantom\rule0ex0ex=\phantom\rule0ex0ex\ensuremathε/3, solving the discrepancy with simulations. For long range elasticity \ensuremathζ\phantom\rule0ex0ex=\phantom\rule0ex0ex\frac\ensuremathε3(1+0.39735\ensuremathε), \ensuremathε\phantom\rule0ex0ex=\phantom\rule0ex0ex2\ensuremath-d, much closer to the experimental value ( \ensuremath≈0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.