Domain walls and chaos in the disordered SOS model

Details Domain walls and chaos in the disordered SOS model Domain walls and chaos in the disordered SOS model

2009-05-29

arxiv.org/abs/0905.4816v1

J. Stat. Mech., P08022 (2009)

Physics

Condensed Matter

Disordered Systems and Neural Networks

23 pages, 11 figures

Scientific paper

10.1088/1742-5468/2009/08/P08022

Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's left passage formula with kappa=4 whereas their fractal dimension is d_s=1.25, and therefore is NOT described by "Stochastic-Loewner-Evolution" (SLE). Optimal droplets with a lateral size between L and 2L have the same fractal dimension as domain walls but an energy that saturates at a value of order O(1) for L->infinity such that arbitrarily large excitations exist which cost only a small amount of energy. Finally it is demonstrated that the sensitivity of the ground state to small changes of order delta in the disorder is subtle: beyond a cross-over length scale L_delta ~ 1/delta the correlations of the perturbed ground state with the unperturbed ground state, rescaled by the roughness, are suppressed and approach zero logarithmically.

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