Above that line the function $Z_4(x,y,z)$ diverges.[]{data-label="kappa-exp"}](figure3.eps){width="3in"}

Divergence of $Z_4(x,y,z)$ for $\varkappa < 1$ is not a unique feature of the power law correlation function and also takes place for faster decaying correlation functions $c(x)$, for example, such as $c(x)=\exp\left[-(x/a)^n\right]$ with $n < 1$, see Fig. \[kappa-exp\]. For the pure exponential correlation function with $n=1$ $Z_4(x,y,z)$ always converges for $\varkappa <1$ (see ). Exponential function separates correlation functions permitting the development of the anomalous diffusion for some $\varkappa < 1$ from those giving only the normal diffusion: correlation functions decaying faster then the exponential one, always have the finite $D$ for $\varkappa <1$. This statement can be easily verified analytically for the finite range correlation function $c(x)=\theta(a-x)$ or numerically for the Gaussian correlation function $c(x)=\exp\left[-(x/a)^2\right]$.

Numerical evaluation of $\varkappa_c$ reveals also that for every tested correlation function $c(x)$ the solution of for the minimal (critical) $\varkappa$ is achieved for $y\rightarrow\infty$. Note that variable $y$ is unique with respect to this feature, it not valid for $z$ and $x$ which remain finite. This particular property is related to the structure of $Z_4(x,y,z)$: in the term $U(x+y)$ enters the exponent with the plus sign. The random energy $U(x+y)$ is negative in all 