Crossover Scaling Functions in One Dimensional Dynamic Growth Models

The crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang (KPZ) type growth is studied for the body-centered solid-on-solid model. The time needed to reach the stationary state $l_t$ is expected to be proportional to the growth parameter $s$, $l_t^{-1\mathrm{}}\simeq \frac{\mathrm{As}}{N^{\mathrm{zkpz}}}$, with $N$ the system size and $A$ a universal amplitude. This implies that the crossover exponent is equal to the change in the dynamic exponent. We predict the general form of the crossover scaling function. The mass gaps at $N\le 18$ confirm this within 0.5% for all values of $s$. We also point out that KPZ type growth is equivalent to a phase transition in mesoscopic metallic rings where attractive interactions destroy the persistent current, and to end points of facet ridges in equilibrium crystal shapes.