  The scaling of turbulent heat flux with respect to electrostatic potential is
examined in the framework of a reduced ($4$D) kinetic system describing
electrostatic turbulence in magnetized plasmas excited by the ion temperature
gradient instability. Numerical simulations were instigated by, and tested the
predictions of generic renormalized turbulence models like the $2$D fluid model
for electrostatic turbulence [Y.~Z.~Zhang and S.~M.~Mahajan, Phys.~Fluids B 5
(7), pp.~2000 (1993)]. A fundamental, perhaps, universal result of this
theory-simulation combination is the demonstration that there exist two
distinct asymptotic states (that can be classified as Weak turbulence (WT) and
Strong turbulence (ST) states) where the turbulent diffusivity $Q$ scales quite
differently with the strength of turbulence measured by the electrostatic
energy $\|\phi\|^2$. In the case of WT $Q \propto \|\phi\|^2$, while in ST $Q$
has a weaker dependence on the electrostatic energy and scales as $\|\phi\|$.
