Statistical Topography of Glassy Interfaces

TL;DR

This paper investigates the statistical properties of two-dimensional glassy interfaces with quenched disorder, revealing how disorder type influences geometrical exponents and confirming scaling relations for self-affine surfaces.

Contribution

It introduces a novel analysis of interface topography using combinatorial optimization and finite-size scaling, highlighting disorder-dependent and disorder-independent geometrical exponents.

Findings

Contour-loop exponents vary with disorder type

Scaling relations hold for self-affine rough surfaces

Fully packed loop exponents are unaffected by disorder

Abstract

Statistical topography of two-dimensional interfaces in the presence of quenched disorder is studied utilizing combinatorial optimization algorithms. Finite-size scaling is used to measure geometrical exponents associated with contour loops and fully packed loops. We find that contour-loop exponents depend on the type of disorder (periodic ``vs'' non-periodic) and they satisfy scaling relations characteristic of self-affine rough surfaces. Fully packed loops on the other hand are unaffected by disorder with geometrical exponents that take on their pure values.