Kardar-Parisi-Zhang universality class in (d+1)-dimensions

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Nonlinear Dynamics

Background:

• The Kardar-Parisi-Zhang (KPZ) class describes the dynamics of growing surfaces.
• Determining the exact scaling exponents in different substrate dimensions (d) remains a significant challenge.

Purpose of the Study:

• To analytically derive the exact KPZ growth exponents (βd) as a function of substrate dimension.
• To validate the derived exponents through computational and theoretical methods.

Main Methods:

• Analytical derivation based on dimensional analysis of related growth equations.
• Extensive Monte Carlo simulations of discrete growth models.
• Real-space renormalization group (RG) calculations for directed polymers in random media (DPRM).

Main Results:

• A novel analytical formula for KPZ growth exponents: βd=7/8d+13.
• Excellent agreement between the derived exponents and existing literature estimates.
• Confirmation of the analytical results via Monte Carlo simulations and RG calculations up to d=15.
• Left-tail exponents of DPRM energy distributions further verify the analytical findings.

Conclusions:

• The proposed analytical formula provides an accurate and general solution for KPZ growth exponents across dimensions.
• The findings resolve a long-standing open problem in statistical physics.
• This work offers a new perspective on surface growth phenomena and disordered systems.