Maximum relative height of elastic interfaces in random media

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Materials Science

Background:

• Self-affine interfaces in random potentials are crucial in understanding phenomena like fracture and wetting.
• The maximal relative height (MRH) distribution characterizes interface configurations, particularly at depinning transitions.
• Previous work established the Gaussian independent modes approximation for average width distributions.

Purpose of the Study:

• To analyze the maximal relative height (MRH) distribution of 1D self-affine elastic interfaces in random potentials.
• To compare MRH distributions for ground-state and critical depinning configurations across different universality classes.
• To evaluate the accuracy of the Gaussian independent modes approximation for MRH distributions.

Main Methods:

• Exact numerical sampling of interface configurations.
• Analysis of ground-state (zero driving force) and critical (depinning threshold) configurations.
• Comparison with distributions generated by independent Fourier modes; analytical derivation using Pickands' theorem for right tails.

Main Results:

• MRH distributions are generally sensitive to boundary conditions.
• Corrections from the Gaussian independent modes approximation are typically small.
• For the random-periodic class ground state with periodic boundary conditions, the MRH distribution converges to the Airy distribution in the large size limit.

Conclusions:

• The Gaussian independent modes approximation provides a reasonable, though not perfect, description of MRH distributions.
• Boundary conditions play a significant role in shaping the MRH distribution.
• The convergence to the Airy distribution in a specific limit highlights a fundamental behavior of these interface systems.