Anomalous scaling in depinning transitions

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Non-equilibrium Systems

Background:

• Depinning transitions are critical phenomena observed in systems with interfaces driven across disordered media.
• Renormalization group (RG) theory is a powerful tool for studying critical phenomena, including depinning transitions.
• Self-organized criticality (SOC) describes systems that naturally evolve to a critical state.

Purpose of the Study:

• To investigate the universality of renormalization group (RG) flows for depinning transitions.
• To compare RG results with self-organized critical (SOC) models.
• To analyze the behavior of scaling functions near the critical point under different driving conditions.

Main Methods:

• Application of renormalization group (RG) techniques to analyze depinning transitions.
• Comparison of RG results with theoretical models of self-organized criticality (SOC).
• Analysis of scaling functions and critical exponents under constant force and constant velocity driving.

Main Results:

• RG flows for depinning transitions are independent of whether the driving force or system velocity is held constant.
• Scaling functions near the critical point exhibit crossover to forms with singular behavior, differing between constant force and constant velocity driving.
• Apparent critical exponents can vary depending on the driving mode, as demonstrated by comparing extremal dynamics with RG results.

Conclusions:

• The universality of RG flows in depinning transitions is confirmed, allowing for comparisons with SOC models.
• Singular behaviors in scaling functions near the critical point require careful consideration of the driving mode.
• Accurate comparisons between RG and SOC models necessitate accounting for the distinct apparent critical exponents arising from different driving conditions.