Universal scaling relation for growth phenomena
Statistical Mechanics
2025-03-18 v1
Abstract
The Family-Vicsek relation is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this work, we revisit the scaling analysis and, through both analytical and computational means, show that the Family-Vicsek relation can be generalized to a new scaling independent of the size, substrate dimension , and scaling exponents. We use properties of lattice growth models in the Kardar-Parisi-Zhang and Villain-Lai-Das Sarma universality classes for to support our claims.
Keywords
Cite
@article{arxiv.2503.12500,
title = {Universal scaling relation for growth phenomena},
author = {Evandro A. Rodrigues and Edwin E. Mozo Luis and Thiago A. de Assis and Fernando A. Oliveira},
journal= {arXiv preprint arXiv:2503.12500},
year = {2025}
}