Ground state properties of solid-on-solid models with disordered substrates

TL;DR

This paper investigates the ground state properties of solid-on-solid models with disordered substrates, revealing their marginal stability and fractal characteristics through exact solutions and correlation analysis.

Contribution

It introduces a new minimum cost flow algorithm to determine exact ground states and analyzes their stability and fractal nature in disordered solid-on-solid models.

Findings

Domain wall energy grows logarithmically with system size

Ground states show marginal stability

Fractal dimension of steps estimated

Abstract

We study the glassy super-rough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a newly developed minimum cost flow algorithm. Results for the height-height correlation function are compared with analytical and numerical predictions. The domain wall energy of a boundary induced step grows logarithmically with system size, indicating the marginal stability of the ground state, and the fractal dimension of the step is estimated. The sensibility of the ground state with respect to infinitesimal variations of the quenched disorder is analyzed.