$c(x)\propto 1/x^{1/2}$, where $\Delta D$ is nonzero, the diffusivity is sensitive to the sign of $c(x)$, in striking contrast to the average velocity $v$.

![Different domains in $n-\varkappa$ plane for the power law correlation function (\[phase-power\]). Finite diffusivity does exist in the domain 1, while in the domains $2 - 4$ the anomalous diffusion takes place (see more detailed explanation in the text). Insert shows the result of the analytical calculation of the dividing line $\varkappa=\varkappa_c(n)$ between domains 1 and 2 according to (solid line) and numerical calculation of $\varkappa_c(n)$ (points). We neglect here the difference between $\varkappa_c+1$ and 2.[]{data-label="kappa-power-law"}](figure2.eps){width="3in"}

In addition, hints for the possibility for $\det \textbf{T}$ becomes negative for $\varkappa < 1$, while for the exponential function $c(x)$ this is not possible. Nonpositivity of $\det \textbf{T}$ means that the correlation function $Z_4(x,y,z)$ diverges and, hence, the diffusivity does not exists, too (this is previously mentioned mechanism II). Fig. \[kappa-power-law\] shows the phase diagram for the power law correlation function $$c(x)=\frac{1}{(x/a)^n+1},
\label{phase-power}$$ i.e. the regions in the plane $n-\varkappa$ where the diffusivity does exist or not exist. In Fig. \[kappa-power-law\] the vertical line at $n=1/2$ separates the domain $n< 1/2$ where $D$ does not exist for any $\varkappa 