title: Renormalization of pinned elastic systems: how does it work beyond one loop?
abstract: We study the field theories for pinned elastic systems at equilibrium and at depinning. Their beta functions differ to two loops by novel "anomalous" terms. At equilibrium we find a roughness zeta = 0.208 298 04 epsilon + 0.006 858 epsilon(2) (random bond), zeta = epsilon/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find zeta = epsilon/3(1 + 0.143 31 epsilon), epsilon = 4 - d, in violation of the conjecture zeta = epsilon/3, solving the discrepancy with simulations. For long range elasticity zeta = epsilon/3(1 + 0.397 35 epsilon), epsilon = 2 - d, much closer to the experimental value (approximately 0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.
authors: CNRS-Laboratoire de Physique des Solides, Université de Paris-Sud, Orsay, France.
authors: P
authors: P
authors: Chauve
authors: P
authors: P
authors: Le Doussal
authors: K J
authors: KJ
authors: Wiese