Correlations of a bound interface over a random substrate

TL;DR

This study uses Monte-Carlo simulations to analyze the correlation function of a one-dimensional interface over a random substrate, revealing a specific exponential decay form with a variable exponent influenced by interface tension.

Contribution

It provides a detailed numerical characterization of the height correlation function and its dependence on interface tension, which was not previously well understood.

Findings

Correlation function fits exp(-(j/b)^c) form

Exponent c varies from 1.0 to 1.5 with tension

High-precision fit across full correlation range

Abstract

The correlation function of a one-dimensional interface over a random substrate, bound to the substrate by a pressure term, is studied by Monte-Carlo simulation. It is found that the height correlation < h_i ; h_{i+j} >, averaged over the substrate disorder, fits a form exp(-(j/b)^c) to a surprising precision in the full range of j where the correlation is non-negligible. The exponent c increases from 1.0 to 1.5 when the interface tension is taken larger and larger.