Non-universal finite size scaling of rough surfaces

TL;DR

This paper investigates the non-universal finite size scaling behavior in a (1+1)D nonlinear growth model with extended particles, revealing multiple crossover regimes and size-dependent roughness exponents, challenging the universality of scaling functions.

Contribution

It introduces a new scaling relation combining two functions for different regimes and highlights the size dependence of roughness exponents in surface growth.

Findings

Identification of three distinct crossover regions in height fluctuation.

Violation of universal scaling function for height fluctuations.

Dependence of roughness exponents on system size.

Abstract

We demonstrate the non-universal behavior of finite size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in generalized point of view. In particular, we show the violation of the universal nature of the scaling function corresponding to the height fluctuation in (1+1) dimension. The 2nd order moment of the height fluctuation shows three distinct crossover regions separated by two crossover time scales namely, tx1 and tx2. Each regime has different scaling property. The overall scaling behavior is postulated with a new scaling relation represented as the linear sum of two scaling functions valid for each scaling regime. Besides, we notice the dependence of the roughness exponents on the finite size of the system. The roughness exponents corresponding to the rough surface is compared with the growth rate or the velocity of the surface.