Hyperuniformity in the Manna Model, Conserved Directed Percolation and Depinning.

Area of Science:

• Statistical Physics
• Complex Systems
• Condensed Matter Physics

Background:

• Hyperuniformity describes materials with suppressed large-scale density fluctuations, characterized by a structure factor S(q)∼q^{α}.
• Conserved directed percolation (CDP) is a universality class relevant to various physical systems, including the Manna model.
• Interface depinning describes the motion of interfaces in disordered media.

Purpose of the Study:

• To establish an exact relationship between hyperuniformity in conserved directed percolation (CDP) and interface position at depinning.
• To derive a general formula for the hyperuniformity exponent (α) in terms of the dimension (d) and the roughness exponent (ζ) at depinning.
• To provide highly precise results for hyperuniformity in CDP across different dimensions.

Main Methods:

• An exact mapping was established between the density field (n) in CDP and the interface position (u) at depinning: n(x)=n_{0}+∇^{2}u(x).
• The hyperuniformity exponent (α) was derived using this mapping: α=4-d-2ζ.
• Numerical simulations were performed, particularly in d=1, to validate the theoretical predictions.

Main Results:

• The derived formula α=4-d-2ζ accurately predicts hyperuniformity exponents for CDP across various dimensions.
• In d=1, the hyperuniformity exponent is found to be exactly α=1/2.
• For other dimensions (d>1), the exponent satisfies 0.6>α≥0, aligning with existing simulations but offering higher precision.

Conclusions:

• An unexpected and exact connection exists between conserved directed percolation and interface depinning phenomena.
• The study provides a novel framework for understanding hyperuniformity and depinning, yielding precise quantitative predictions.
• The findings correct previous theoretical and simulation results for hyperuniformity in CDP, especially in one dimension.