Domain walls and chaos in the disordered SOS model

Abstract

Domain walls, optimal droplets and disorder chaos at zero temperature are studied numericallyfor the solid-on-solid model on a random substrate. It is shown that the ensemble ofrandom curves represented by the domain walls obeys Schramm’s left passage formula withκ = 4 whereas theirfractal dimension is ds = 1.25, and therefore their behavior cannot be described as showing ‘Schramm– (orstochastic) Loewner evolution’ (SLE). Optimal droplets with a lateral size betweenL and2L have the same fractal dimension as domain walls but an energy that saturates at a value oforder for 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 orderδ in the disorder is subtle: beyond a crossover length scaleLδ∼δ−1 the correlations of the perturbed ground state with the unperturbed ground state, rescaledusing the roughness, are suppressed and approach zero logarithmically.