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Universal and nonuniversal features in the crossover from linear to nonlinear interface growth
T J Oliveira1, K Dechoum, J A Redinz
1Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói RJ, Brazil. tiagojo@if.uff.br
Summary
This study reveals a crossover in interface growth models from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang (KPZ) scaling. A linear relationship for the nonlinear term coefficient was analytically derived and numerically confirmed.
Area of Science:
- Physics
- Condensed Matter Physics
- Statistical Mechanics
Background:
- The study investigates a restricted solid-on-solid model for surface growth.
- It focuses on systems with deposition and evaporation dynamics.
Purpose of the Study:
- To analyze the crossover behavior between Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) scaling in a 1D substrate.
- To derive and verify the associated Kardar-Parisi-Zhang (KPZ) equation and its nonlinear term coefficient.
Main Methods:
- Analytical derivation of the KPZ equation for the model.
- Numerical calculation of tilt-dependent growth velocities for various deposition/evaporation probabilities (p).
- Identification of interface roughness scaling regimes and estimation of crossover times (tc).
Main Results:
- A crossover from EW to KPZ scaling occurs near p = 0.5.
- The nonlinear coefficient (lambda) is linearly proportional to (p - 1/2), contrasting with parabolic laws in other models.
- Crossover times (tc) scale with lambda^-phi, yielding phi = 4.1 ± 0.1, consistent with theoretical predictions.
Conclusions:
- The model exhibits a distinct linear relationship for the KPZ nonlinear term coefficient.
- The study provides accurate numerical estimates for crossover exponents, supporting universal theoretical values.
- This work clarifies scaling behaviors in models with competing growth mechanisms.