Crossover Scaling Functions in One Dimensional Dynamic Growth Models

TL;DR

This paper investigates the crossover from Edwards-Wilkinson to KPZ growth in a one-dimensional model, providing exact numerical calculations and predicting the crossover scaling functions, with implications for phase transitions and crystal shapes.

Contribution

It offers the first exact numerical analysis of the crossover scaling functions in the BCSOS model and predicts their structure, connecting growth models to phase transition phenomena.

Findings

Exact numerical values for mass gaps up to N=18

Predicted crossover scaling functions for the model

Confirmed numerical relations for mass gaps

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.