Renormalization of pinned elastic systems: how does it work beyond one loop ?

Pascal Chauve¹, Pierre Le Doussal², Kay Jörg Wiese³
¹CNRS-Laboratoire de Physique des Solides, Université de Paris-Sud, Bât. 510, 91405 Orsay France
²CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
³Fachbereich Physik, Universität Essen, 45117 Essen, Germany

Abstract

We study the field theories for pinned elastic systems at equilibrium and at depinning. Their β-functions differ to two loops by novel ``anomalous'' terms. At equilibrium we find a roughness ζ = 0.20829804 ε + 0.006858 ε² (random bond), ζ = ε/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find ζ = ε/3(1 + 0.14331 ε), ε = 4-d, in violation of the conjecture ζ = ε/3, solving the discrepancy with simulations. For long range elasticity ζ = ε/3(1 + 0.39735 &epsilon), ε = 2-d, much closer to the experimental value (≈ 0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.

cond-mat/0006056 [pdf]
Phys. Rev. Lett. 86 (2001) 1785 [pdf]