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

In an artificial 3D percolation nano medium, the clusters filled by the Ising magnets give rise to a topologically nontrivial magnetic structure, leading to new features of the ferromagnetic phase transition without an external magnetic field. In such an inhomogeneous system, the standard Ising model is strongly modified by the spatial percolation cluster distribution. We found numerically that at percolation occupation probability $p<1$ far from the percolation threshold $p_{c3D}$, the magnetization shows ferromagnetic-paramagnetic phase transition with the transition temperature $T_{c}$ depending considerably on the 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.