36th M. Smoluchowski Symposium on Statistical Physics: Soft Matter, Information Processing and Nonequilibrium Fluctuations

Universal scaling relation for growth phenomena

27 Sept 2023, 09:40

40m

Faculty of Physics, Astronomy and Applied Computer Science; Jagiellonian University

Invited Talk Session 9

Speaker

Fernando Oliveira (Universidade de Brasília)

Description

The Family-Vicsek relation [1] is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this Letter, 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 lateral size, substrate dimension $d$, and scaling exponents. This is part of universal behavior, since scaling [2], renormalization and fractals [3-7] are connected. We use properties of the Edwards-Wilkinson and lattice models in the Kardar-Parisi-Zhang and Villain-Lai-Das Sarma universality classes for $1 \leq d \leq 3$ to support our claims.

References

[1] F. Family and T. Vicsek, Journal of Physics A: Mathematical and General 18, L75 (1985).

[2] F. A. Oliveira, B. A. Mello, and I. M. Xavier, Phys. Rev.E 61, 7200 (2000).

[3] M. S. Gomes-Filho and F. A. Oliveira, EPL 133, 10001 (2021)

[4] P. R. H. dos Anjos, W. S. Alves, M. S. Gomes-Filho, D. L. Azevedo and F. A. Oliveira, Frontiers in Physics 9, 741590 (2021).

[5] M. S. Gomes-Filho, A. L. A. Penna and F. A. Oliveira, Results in Physics 26, 104435 (2021).

[6] E. E. M. Luis, T. A. de Assis, F. A. Oliveira, Journal of Statistical Mechanics: Theory and Experiment 8, 083202 (2022).

[7] E. E. Mozo Luis, F. A. Oliveira, and T. A. de Assis,
Phys. Rev. E 107, 034802 (2023).