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The effect of the correlations in the diluteness pattern in the systems withnon-integral dimensionality, on $\nu=\frac{4}{5}$ superdiffusion process isconsidered in this paper. These spatial correlations have proved to be veryeffective in the critical phenomena. To simulate the particles motion in thisprocess, we employ the loop erased random walk (LERW). The spatial correlationsbetween imperfections (site-diluteness) also have been modeled by the Isingmodel on a square lattice. It models the forbidden regions into which theparticles are not allowed to enter. The correlations are controlled by anartificial temperature $T$. The trace of the walkers is shown to beself-similar, whose fingerprint is the power-law behaviors. The detailedanalysis of the random walker's traces reveal that the (Ising-type)correlations affect their geometrical properties. At the critical artificialtemperature $T_c$ we observe that the exponent of end-to-end distance $\nu$becomes $0.807\pm 0.002$. The fractal dimension of the walker's trace is theother geometrical quantity which scales inversely with the square root of thecorrelation length of the Ising model, i.e. $D_f(T)-D_f(T_c)\sim\zeta^{-\alpha}$ in which $\alpha=0.43\pm 0.05$. The winding angle test alsoreveals that the traces are compatible with the Schramm-Loewner evolutiontheory, and the diffusivity parameter for $T=T_c$ is $\kappa=1.89\pm 0.05$.

Correlation effects in the diluteness pattern in non-integral dimensional systems on $\nu=\frac{4}{5}$ superdiffusion process