Width distributions and the upper critical dimension of Kardar-Parisi-Zhang interfaces

Simulations of restricted solid-on-solid growth models are used to build the width distributions of $d=2\mathrm{}–5$ dimensional Kardar-Parisi-Zhang (KPZ) interfaces. We find that the universal scaling function associated with the steady-state width distribution changes smoothly as d is increased, thus strongly suggesting that $d=4\mathrm{}$ is not an upper critical dimension for the KPZ equation. The dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity.