Domain walls and chaos in the disordered SOS model

Abstract

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 κ = 4 whereas their fractal dimension is ds = 1.25, and therefore their behavior cannot be described as showing Schramm (or 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 → ∞ 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 δ in the disorder is subtle: beyond a crossover length scale Lδ ∼ δ−1 the correlations of the perturbed ground state with the unperturbed ground state, rescaled using the roughness, are suppressed and approach zero logarithmically.