Crossover Scaling Functions in One Dimensional Dynamic Growth Models.pdf

CROSSOVER SCALING FUNCTIONS IN ONE DIMENSIONAL DYNAMIC GROWTH MODELS John Neergaard and Marcel den Nijs Department of Physics University of Washington 4 9 Seattle, WA 98195 9 1 n u J 1 2 The crossover from Edwards-Wilkinson (s = 0) to KPZ (s 0) type growth is 1 studied for the BCSOS model. We calculate the exact numerical values for the k = 0 v 6 and 2π/N massgap for N ≤ 18 using the master equation. We predict the structure 8 2 0 of the crossover scaling function and confirm numerically that m0 ≃ 4(π/N ) [1 + 6 2 2 0.5 2 2 2 0.5 0 3u (s)N/(2π )] and m1 ≃ 2(π/N ) [1 + u (s)N/π ] , with u(1) = 1 4 KPZ type growth is equivalent to a phase transition in meso-scopic metallic rings 9 / where attractive interactions destroy the persistent current; and to endpoints of t a m facet-ridges in equilibrium crystal shapes. - d n o c : v i X r a 1 A large amount of theoretical effort has been devoted in recent years to establish and classify the scaling properties of dynamic processes such as those at growing interfaces. Several dynamic universality classes have emerged. One of them is the so-called KPZ universality class, named after the non-linear Langevin equation studied by Kardar, Parisi, and Zhang [1]. Older examples are Edwards-Wilkinson (EW) growth [2] and directed percolation [3]. They are distinguished by the value of the dynamic critical exponent z; characteristic lengths and times scale as t ∼ lz . Most of the evidence is numerical in nature, in particular f