Ground-State Roughness of the Disordered Substrate and Flux Line in d=2

TL;DR

This paper uses efficient optimization algorithms to study the ground-state roughness of disordered crystalline surfaces and flux lines in two dimensions, revealing a super-rough state characterized by a squared logarithmic growth of interface width.

Contribution

It introduces polynomial-time algorithms for finding ground states, enabling detailed analysis of interface roughness in disordered systems.

Findings

Evidence for a $ abla^2(L)$ super-rough state at low temperatures

Large-scale simulations up to 420^2 size

Analysis based on over 2000 realizations per size

Abstract

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using $d=2$ systems up to size $420^2$, with a minimum of $2 \times 10^3$ realizations at each size, we find very strong evidence for a $\ln^2(L)$ super-rough state at low temperatures.