Crossover Scaling Functions in One Dimensional Dynamic Growth Models

Abstract

The crossover from Edwards-Wilkinson ($s=0$) to KPZ ($s>0$) type growth is studied for the BCSOS model. We calculate the exact numerical values for the $k=0$ and $2\pi /N$ massgap for $N\le 18$ using the master equation. We predict the structure of the crossover scaling function and confirm numerically that $m_0\simeq 4(\pi /N{)}^2[1+3u^2(s)N/(2{\pi }^2){]}^{0.5}$ and $m_1\simeq 2(\pi /N{)}^2[1+u^2(s)N/{\pi }^2{]}^{0.5}$, with $u(1)=1.03596967$. KPZ type growth is equivalent to a phase transition in meso-scopic metallic rings where attractive interactions destroy the persistent current; and to endpoints of facet-ridges in equilibrium crystal shapes.

11 pages, TeX, figures upon request

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