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Phase transition in the 2D ballistic growth model with quenched disorder

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  • Benoit, Magali
  • Jullien, Rémi

Abstract

Quenched disorder is introduced in the two dimensional ballistic growth model by randomly distributing growing rates equal to ϵ and 1 on the sites of a square lattice with probabilities p and 1 - p. The model is studied by means of numerical simulations in a strip geometry of width up to L = 2048 and heights up to 15L with periodic boundary conditions at the edges of the strip. Numerical results on the bulk density and the surface thickness are consistent with the existence of a phase transition in the limit ϵ → 0, L → ∞, at a critical value p∗ = 0.305±0.001. It is shown that the fraction of ϵ-rate sites, included in the bulk during the growth process, can be considered as an order parameter. Critical exponents are estimated and are found to be different than for the Eden model in the same random environment.

Suggested Citation

  • Benoit, Magali & Jullien, Rémi, 1994. "Phase transition in the 2D ballistic growth model with quenched disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 207(4), pages 500-516.
    • Handle: RePEc:eee:phsmap:v:207:y:1994:i:4:p:500-516
    DOI: 10.1016/0378-4371(94)90207-0
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    References listed on IDEAS

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    1. Bunde, Armin & Gouyet, Jean-François, 1985. "Brownian motion in the bistable potential at intermediate and high friction: Relaxation from the instability point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 357-374.
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