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

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

2000-06-04

arxiv.org/abs/cond-mat/0006056v2

Phys. Rev. Lett. 86 (2001) 1785

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevLett.86.1785

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 $\zeta=0.20829804 \epsilon + 0.006858 \epsilon^2$ (random bond), $\zeta=\epsilon/3$ (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find $\zeta=\frac{\epsilon}{3}(1 + 0.14331 \epsilon)$, $\epsilon=4-d$, in violation of the conjecture $\zeta=\epsilon/3$, solving the discrepancy with simulations. For long range elasticity $\zeta=\frac{\epsilon}{3}(1 + 0.39735 \epsilon)$, $\epsilon=2-d$, 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.

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