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

TL;DR

This paper investigates how the ferromagnetic phase transition in a 3D percolating nano system with fractal clusters is influenced by the cluster structure and percolation probability, revealing a dependence of transition temperature on fractal dimension.

Contribution

It introduces a numerical study of the Ising model on a 3D percolating nano medium with noninteger fractal dimension, highlighting the impact of inhomogeneity on phase transition behavior.

Findings

Magnetization exhibits a ferromagnetic-paramagnetic transition at various temperatures depending on p.

Transition temperature T_c varies significantly with percolation probability p.

Near the percolation threshold, T_c is affected by the fractal dimension of the incipient cluster.

Abstract

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.