Large-scale simulations of ballistic deposition: The approach to asymptotic scaling

Extensive kinetic Monte Carlo simulations are presented for ballistic deposition (BD) in (1+1) dimensions. Asymptotic scaling is found only for lattice sizes L≳2¹². Such a large system size for the onset of scaling explains the widespread discrepancies of previous reports for exponents of BD in one and likely higher dimensions. The exponents obtained from our simulations, α=0.499±0.004 and β=0.336±0.004, are in excellent agreement with the exact values α=½ and β=1/3 for the one-dimensional Kardar-Parisi-Zhang equation. Our findings make possible a more informed exploration of exponents for BD in higher dimensions, accurate estimates of which have proven to be elusive.