Exact scaling in competitive growth models

L. A. Braunstein, Chi Hang Lam

Research output: Journal article publicationJournal articleAcademic researchpeer-review

21 Citations (Scopus)


A competitive growth model (CGM) describes the aggregation of a single type of particle under two different growth rules with occurrence probabilities p and 1-p. We explain the origin of the scaling behavior of the resulting surface roughness at small p for two CGM's which describe random deposition (RD) competing with ballistic deposition and RD competing with the Edward-Wilkinson (EW) growth rule. Exact scaling exponents are derived. The scaling behavior of the coefficients in the corresponding continuum equations are also deduced. Furthermore, we suggest that, in some CGM's, the p dependence on the coefficients of the continuum equation that represents their universality class can be nontrivial. In some cases, the process cannot be represented by a unique universality class. In order to show this, we introduce a CGM describing RD competing with a constrained EW model. This CGM shows a transition in the scaling exponents from RD to a Kardar-Parisi-Zhang behavior when p is close to 0 and to a Edward-Wilkinson one when p is close to 1 at practical time and length scales. Our simulation results are in excellent agreement with the analytic predictions.
Original languageEnglish
Article number026128
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 1 Aug 2005

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics


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