Strong-coupling behaviour in discrete Kardar-Parisi-Zhang equations

T. J. Newman, A. J. Bray

    Research output: Contribution to journalArticle

    40 Citations (Scopus)

    Abstract

    We present a systematic discretization scheme for the Kardar-Parisi-Zhang (KPZ) equation, which correctly captures the strong-coupling properties of the continuum model. In particular we show that the scheme contains no finite-time singularities in contrast to conventional schemes. The implications of these results to (i) previous numerical integration of the KPZ equation, and (ii) the non-trivial diversity of universality classes for discrete models of 'KPZ-type' are examined. The new scheme makes the strong-coupling physics of the KPZ equation more transparent than the original continuum version and allows the possibility of building new continuum models which may be easier to analyse in the strong-coupling regime.
    Original languageEnglish
    Pages (from-to)7917-7928
    Number of pages12
    JournalJournal of Physics A: Mathematical and General
    Volume29
    Issue number24
    DOIs
    Publication statusPublished - 21 Dec 1996

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