  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.
