Nonthermal scaling phenomena can exhibit a characteristic dependence on the dimensionality $d$ of space. For $d=3$ and 4 we simulate a relativistic scalar field theory on a lattice and compute turbulent scaling exponents. We recover Kolmogorov or weak wave-turbulence in the perturbative high-momentum regime, where it exhibits the scaling exponent ${\kappa }_w=d-3/2$. In the nonperturbative infrared regime, we find a different scaling exponent ${\kappa }_s=4(5)$ for $d=3(4)$, which is in agreement with the recently predicted anomalously large values ${\kappa }_s=d+1$ of strong turbulence. We show how the latter can be seen to characterize stationary transport of a conserved effective particle number.

• Received 29 December 2010

DOI:https://doi.org/10.1103/PhysRevD.83.085004