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In an artificial 3D percolation nano medium, the clusters filled by the Isingmagnets give rise to a topologically nontrivial magnetic structure, leading tonew features of the ferromagnetic phase transition without an external magneticfield. In such an inhomogeneous system, the standard Ising model is stronglymodified by the spatial percolation cluster distribution. We found numericallythat at percolation occupation probability $p<1$ far from the percolationthreshold $p_{c3D}$, the magnetization shows ferromagnetic-paramagnetic phasetransition with the transition temperature $T_{c}$ depending considerably onthe probability $p$. We provide numerical evidence that in vicinity $p_{c3D}$\the dependence $T_{c}(p)$ is affected by the noninteger fractal dimension$D_{H}(p)$ of the incipient percolation spanning cluster.

Critical behavior of Ising spins in a tridimensional percolating nano system with noninteger fractal dimension