Functional renormalization group for anisotropic depinning and relation to branching processes

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics

Background:

• Elastic objects in disordered media exhibit depinning transitions.
• Anisotropy and disorder correlations significantly influence depinning phenomena.
• The Kardar-Parisi-Zhang (KPZ) equation describes the dynamics of interfaces.

Purpose of the Study:

• To investigate the generation of the KPZ term in anisotropic systems using the functional renormalization group.
• To analyze the role of nonanalytic disorder distributions in the depinning mechanism.
• To study the behavior of elastic manifolds in both periodic and nonperiodic disorder with varying elasticity ranges.

Main Methods:

• Application of the functional renormalization group (FRG) to study elastic object depinning.
• Explicit computation of the beta function to one loop, incorporating nonanalyticity.
• Utilizing a Cole-Hopf-transformed theory to analyze the KPZ coupling to all orders.
• Analysis of flow equations for different elasticity ranges (short-range and long-range).

Main Results:

• The Kardar-Parisi-Zhang (KPZ) term is shown to be universally generated by anisotropy, except when symmetry forbids it.
• A two-step mechanism involving nonanalytic disorder distributions beyond the Larkin length generates the KPZ term.
• New terms in the beta function are identified due to proper treatment of nonanalyticity.
• The KPZ coupling is found to be uncorrected to all orders.
• Several transient fixed points are identified, all leading to a runaway flow dominated by a Landau-ghost mode.
• For long-range elasticity, two phases are identified based on KPZ coupling strength.
• A 3D invariant subspace is identified for short-range elasticity, encompassing fixed points and the Landau mode.

Conclusions:

• The study provides a comprehensive understanding of KPZ term generation in anisotropic depinning systems.
• The identified fixed points and runaway flow dynamics offer insights into the upper critical dimension.
• The findings are relevant for diverse physical systems, including charge density waves and contact line depinning.
• The connection to branching and reaction-diffusion processes highlights broader implications.