A Renormalization Scheme and Skewness of Height Fluctuations in $(1+1)$-dimensional VLDS Dynamics

Abstract

We study the $(1+1)$-dimensional Villain, Lai, and Das Sarma (VLDS) equation driven by a Gaussian white noise and implement a renormalization scheme without rescaling at one-loop order. Using a diagrammatic method, we calculate the renormalized second and third moments in the large-scale and long-time limits. The ensuing skewness value is $S=-0.0441$. This (negative) value is consistent with the numerical prediction of Das Sarma \emph{et al.} [Phys. Rev. E {\bf 53} 359 (1996)].

20 pages, 4 figures, version accepted in J. Stat. Mech.:Theory and Exp

References in corpus (2)

• Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth
• Kurtosis of height fluctuations in $(1+1)$ dimensional KPZ Dynamics

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