Relaxation to steady states and dynamical exponents in deposition models

TL;DR

This paper investigates the relaxation dynamics and estimates the dynamical exponents in various deposition models with limited mobility, using a new method to analyze the crossover time to saturation.

Contribution

It introduces a method to calculate characteristic relaxation times and dynamical exponents in deposition models, improving accuracy over previous approaches.

Findings

Effective exponents z_L converge to continuum theory values.

Estimated z=2 for 2D Family model.

Obtained z≈1.6 for 2D RSOS model.

Abstract

Considering some deposition models with limited mobility, we show that the typical decay of the interface width to its saturation value is exponential, which defines the crossover or saturation time \tau. We present a method to calculate a characteristic time \tau_0 proportional to \tau and estimate the dynamical exponent z. In one dimensional substrates of lengths L <~ 2048, the method is applied to the Family model, the restricted solid-on-solid (RSOS) model and the ballistic deposition. Effective exponents z_L converge to asymptotic values consistent with the corresponding continuum theories. For the two-dimensional Family model, the expected dynamic scaling hypothesis suggests a particular definition of \tau_0 that leads to z=2, improving previous calculations based on data collapse methods. For the two-dimensional RSOS model, we obtain z ~ 1.6 and \alpha < 0.4, in agreement with recent large scale simulations.