Numerical study of the disorder-driven roughening transition in an elastic manifold in a periodic potential

TL;DR

This paper studies the transition from flat to rough phases in a 3+1D elastic manifold influenced by disorder and periodic potential, using numerical methods to estimate critical behavior at zero temperature.

Contribution

It provides the first numerical analysis of the disorder-driven roughening transition in a 3+1D elastic manifold with a periodic potential, including critical exponents estimation.

Findings

Identifies a continuous phase transition between flat and rough phases.

Estimates critical exponents for the transition.

Compares numerical results with analytical predictions.

Abstract

We investigate the roughening phase transition of a $(3+1)$-dimensional elastic manifold driven by the completion between a periodic pinning potential and a randomly distributed impurities. The elastic manifold is modeled by a solid-on-solid type interface model, and universal features of the transition from a flat phase (for strong periodic potential) to a rough phase (for strong disorder) are studied at zero temperature using a combinatorial optimization algorithm technique. We find a {\it continuous} transition with a set of numerically estimated critical exponents that we compare with analytic results and those for a periodic elastic medium.