Directed percolation with a conserved field and the depinning transition

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Complex Systems

Background:

• Conserved directed percolation (C-DP) and the depinning transition of disordered elastic interfaces are critical phenomena.
• Recent work established their shared universality class via field theory mapping.
• Understanding these systems is crucial for diverse fields, from material science to network theory.

Purpose of the Study:

• To present an alternative field theoretic derivation of the C-DP functional.
• To re-examine the mapping between C-DP and the quenched Edwards-Wilkinson model.
• To clarify the role of a specific, previously problematic term in the field theory.

Main Methods:

• Coherent-state path integral formulation for C-DP.
• Application of the Grassberger transformation to derive the field theoretic functional.
• Renormalization group analysis to assess the relevance of specific terms.

Main Results:

• An alternative derivation of the C-DP field theoretic functional is presented.
• The Grassberger transformation is shown to avoid disadvantages of the Doi shift.
• A problematic term in the field theoretic functional is demonstrated to be redundant under renormalization group analysis.

Conclusions:

• The study provides a robust alternative derivation for the C-DP field theory.
• The findings reinforce the connection between C-DP and elastic interface depinning.
• The redundancy of the specific term simplifies the theoretical framework and understanding of these critical phenomena.