Crossover Scaling Functions in One Dimensional Dynamic Growth Models
- 30 January 1995
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 74 (5), 730-733
- https://doi.org/10.1103/physrevlett.74.730
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 $N\leq 18$ 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.
Keywords
This publication has 8 references indexed in Scilit:
- Coexistence point in the six-vertex model and the crystal shape of fcc materialsPhysical Review Letters, 1994
- Quantum persistent currents and classical periodic orbitsPhysical Review B, 1993
- Bethe solution for the dynamical-scaling exponent of the noisy Burgers equationPhysical Review A, 1992
- The asymmetric six-vertex modelJournal of Statistical Physics, 1992
- Continuum models of crystal growth from atomic beams with and without desorptionJournal de Physique I, 1991
- Dynamic scaling and phase transitions in interface growthPhysica A: Statistical Mechanics and its Applications, 1990
- A six-vertex model as a diffusion problem: derivation of correlation functionsJournal of Physics A: General Physics, 1990
- Dynamic Scaling of Growing InterfacesPhysical Review Letters, 1986