Strong versus weak wave-turbulence in relativistic field theory

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 κw=d-3/2. In the nonperturbative infrared regime, we find a different scaling exponent κₛ=4(5) for $d=3(4)$, which is in agreement with the recently predicted anomalously large values κₛ=d+1 of strong turbulence. We show how the latter can be seen to characterize stationary transport of a conserved effective particle number.