Fluctuations of self-flattening surfaces

TL;DR

This paper investigates the scaling behavior of self-flattening surfaces, revealing anomalous fluctuations in equilibrium and standard KPZ behavior in nonequilibrium conditions, with analytical insights linking to random walk models.

Contribution

It introduces a restricted solid-on-solid model with global suppression mechanisms and characterizes its scaling properties in different dimensions, providing new analytical understanding.

Findings

Equilibrium surface fluctuations are anomalous with specific exponents in 1D and 2D.

Stationary roughness relates to self-attracting random walk and dimer models.

Nonequilibrium dynamics follow the KPZ universality class.

Abstract

We study the scaling properties of self-flattening surfaces under global suppression on surface fluctuations. Evolution of self-flattening surfaces is described by restricted solid-on-solid type monomer deposition-evaporation model with reduced deposition (evaporation) at the globally highest (lowest) site. We find numerically that equilibrium surface fluctuations are anomalous with roughness exponent $\alpha\simeq 1/3$ and dynamic exponent $z_W \simeq 3/2$ in one dimension (1D) and $\alpha=0 (\log)$ and $z_W \simeq 5/2$ in 2D. Stationary roughness can be understood analytically by relating our model to the static self-attracting random walk model and the dissociative dimer type deposition-evaporation model. In case of nonequilibrium growing/eroding surfaces, self-flattening dynamics turns out to be irrelevant and the normal Kardar-Parisi-Zhang universality is recovered in all dimensions.