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

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 behavior belonging to the two-dimensional Kardar-Parisi-Zhang universality class and find a surface growth exponent: β = 0.2415(15) on 2 17 × 2 17 systems, ruling out β = 1/4 suggested by field theory. The maximum speedup with respect to a single CPU is 240. The steady state has been analyzed by finite size scaling and a growth exponent α = 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 behavior of the steady state scaling function of the interface width.

A KPZ Cocktail-Shaken, not Stirred...

“…9 in that paper. Interestingly, the 2+1 KPZ stationary-state has also permitted a solid multi-model (gDPRM,RSOS,KPZ Euler) estimate β 2+1 =0.241(1), in line with prior gold-medal studies [20,124] at the 3-digit precision level.…”

“…• Recalling recent 2+1 DPRM results [84], which have isolated the higher-dimensional analog of KPZ/TW-GOE, measuring s=0.424 and k=0.346 for the generic pt-plane case, and pinned down the key index ω 2+1 =0.241 [20,124] via a multi-model study [85] of 2+1 KPZ stationary-state statistics, we notice quite similar values for the b=2.3 ♦DPRM, where the exponent, 0.274, might be a little high, but the skewness, 0.423, and kurtosis, 0.372, certainly close to the mark. Given our findings above for the ♦DPRM sk relation, one cannot resist looking at Euclidean KPZ from this same vantage point.…”

Aging of the (2+1)-dimensional Kardar-Parisi-Zhang model

“…Furthermore, this lattice gas can be studied by very efficient simulation methods. Dynamic, bit-coded simulations were run on extremely largesized (L × L) lattice-gas models [37,38], and the surface heights, reconstructed from the slopes…”

“…Throughout this paper we used the estimates from our previous high-precision simulation study [38]: α = 0.393(4), β = 0.2415 (15), and the dynamical scaling exponent z = α/β = 1.627 (26).…”

Keldysh field theory for driven open quantum systems

“…Indeed, the FRG analysis reported in Refs. [252][253][254]277] and numerical simulations [283][284][285][286][287][288][289][290][291][292][293][294][295][296][297] find χ ≈ 0.4 for the value of the roughness exponent, which implies that for |x − x | → ∞ correlations in 2D drivendissipative condensates obey Eq. (236) and not Eq.…”