Depinning in the quenched Kardar-Parisi-Zhang class. I. Mappings, simulations, and algorithm

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• Depinning in disordered media is often modeled by the quenched Edwards-Wilkinson (qEW) equation.
• Anharmonicity and non-potential forces can lead to different depinning behaviors, notably the Kardar-Parisi-Zhang (KPZ) term, creating the quenched KPZ (qKPZ) universality class.

Purpose of the Study:

• To investigate the quenched KPZ (qKPZ) universality class numerically and analytically.
• To demonstrate that the qKPZ class unifies diverse depinning models, including the qKPZ equation, anharmonic depinning, and Tang-Leschhorn cellular automata.
• To establish qKPZ as the effective field theory for these systems.

Main Methods:

• Exact mappings to connect different models within the qKPZ class.
• Development of scaling arguments for critical exponents, including avalanche size and duration.
• Numerical estimation of exponents, effective force correlator, correlation length, effective elasticity, and KPZ nonlinearity.
• Algorithm development for numerical estimation of system parameters.

Main Results:

• The qKPZ universality class, for d=1,2, encompasses the qKPZ equation, anharmonic depinning, and Tang-Leschhorn cellular automata.
• Scaling arguments were developed for critical exponents and avalanche dynamics.
• Numerical estimates for exponents and system-dependent parameters were obtained.
• A universal KPZ amplitude A=1.10(2) was found for d=1 across all studied systems.

Conclusions:

• The quenched KPZ (qKPZ) equation serves as the effective field theory for a range of depinning phenomena in disordered systems.
• The universality of the KPZ amplitude confirms the unifying power of the qKPZ framework.
• This work provides a foundation for further development of field theories for the qKPZ class.