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

Pascal Chauve; Pierre Le Doussal; Kay Wiese

doi:10.1103/PhysRevLett.86.1785

paper

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

arXiv:cond-mat/0006056 · doi:10.1103/PhysRevLett.86.1785

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 $ζ = 0.20829804 ε + 0.006858 ε^{2}$ (random bond), $ζ = ε /3$ (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find $ζ = \frac{ε}{3} (1 + 0.14331 ε)$ , $ε = 4 - d$ , in violation of the conjecture $ζ = ε /3$ , solving the discrepancy with simulations. For long range elasticity $ζ = \frac{ε}{3} (1 + 0.39735 ε)$ , $ε = 2 - d$ , much closer to the experimental value ( $\approx 0.5$ both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.

arXiv commentRevised version, easier to read, 2 tables and comparison with experiments added

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

Abstract

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