Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

Area of Science:

• Statistical Physics
• Complex Systems
• Condensed Matter Physics

Background:

• Interfaces in random media are crucial in diverse physical phenomena.
• Distinguishing between fractal and rough interfaces is a key challenge.
• Universality classes dictate system behavior near critical points.

Purpose of the Study:

• To investigate the universality class of critically pinned interfaces in 2D isotropic random media.
• To determine if fractal and rough interfaces belong to the same universality class.
• To explore the implications for various physical models.

Main Methods:

• Extensive numerical simulations were performed.
• Analysis focused on interfaces with short-range correlations in the randomness.
• The study considered models like random field Ising models and epidemic models.

Main Results:

• A conjecture is proposed that these interfaces are always in the universality class of ordinary percolation.
• No distinction was found between fractal (percolative) and rough, nonfractal interfaces in 2D.
• This holds for zero-temperature random field Ising models, heterogeneous bootstrap percolation, and SIIR epidemics.

Conclusions:

• Critically pinned 2D interfaces in isotropic random media with short-range correlations exhibit universal behavior.
• The findings unify the understanding of interface roughness and fractal properties in these systems.
• Exclusions apply to models with long-range correlations or forbidden overhangs.