Domain walls and chaos in the disordered SOS model

TL;DR

This study numerically investigates the disordered SOS model, revealing that domain walls follow Schramm's formula with specific fractal properties, and explores the energy and chaos characteristics of optimal droplets and ground state sensitivity.

Contribution

It provides the first detailed numerical analysis of domain walls, droplets, and chaos in the disordered SOS model, highlighting deviations from SLE and characterizing energy saturation and ground state sensitivity.

Findings

Domain walls obey Schramm's left passage formula with kappa=4.

Fractal dimension of domain walls is 1.25, not described by SLE.

Large excitations have bounded energy, indicating marginal stability.

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 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.