Roughness of a tilted anharmonic string at depinning

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• The behavior of driven interfaces in random media is a key problem in statistical physics.
• Understanding universality classes, like the Kardar-Parisi-Zhang (KPZ) class, is crucial for describing complex systems.
• Previous work introduced a discretized string model in a 2D random potential.

Purpose of the Study:

• To numerically compute the roughness of a driven string with anharmonic elastic energy.
• To investigate the critical depinning threshold in a uniform applied force.
• To determine if the anharmonic elastic energy leads to a crossover to the quenched KPZ universality class.

Main Methods:

• Utilizing finite size scaling techniques for numerical computation.
• Analyzing a discretized model of a driven string in a two-dimensional random potential.
• Applying a uniform external force and considering a net average tilt.

Main Results:

• The roughness of the string was numerically computed at the critical depinning threshold.
• A crossover to the quenched KPZ universality class was observed due to anharmonic elastic energy.
• The findings align with recent theoretical predictions for such systems.

Conclusions:

• Anharmonic elastic energy is shown to be a critical factor in determining the universality class of driven strings in random potentials.
• The study confirms the transition to the quenched KPZ universality class under specific conditions.
• This research contributes to a deeper understanding of interface dynamics in disordered systems.