Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards

TL;DR

This paper demonstrates large-scale simulations of the 2D Kardar-Parisi-Zhang model using graphics cards, confirming scaling behavior and providing detailed analysis of surface growth exponents, universal functions, and distribution characteristics.

Contribution

The study implements the octahedron model on graphics cards, achieving unprecedented simulation scale and speed, and refines understanding of KPZ universality class exponents and distributions.

Findings

Confirmed KPZ scaling behavior with beta=0.2415(15)

Achieved 240x speed-up over CPU implementations

Determined universal scaling functions and distribution tails

Abstract

The octahedron model introduced recently has been implemented onto graphics cards, which permits extremely large scale simulations via binary lattice gases and bit coded algorithms. We confirm scaling behaviour belonging to the 2d Kardar-Parisi-Zhang universality class and find a surface growth exponent: beta=0.2415(15) on 2^17 x 2^17 systems, ruling out beta=1/4 suggested by field theory. The maximum speed-up with respect to a single CPU is 240. The steady state has been analysed by finite size scaling and a growth exponent alpha=0.393(4) is found. Correction to scaling exponents are computed and the power-spectrum density of the steady state is determined. We calculate the universal scaling functions, cumulants and show that the limit distribution can be obtained by the sizes considered. We provide numerical fitting for the small and large tail behaviour of the steady state scaling function of the interface width.