Fractal dimension in a modified 2D Ising system with regions without spin

Abstract

We investigate the change in dimensionality of an Ising system by increasing the area of a central region without spin, essentially decreasing the density of sites with spin. We describe this change by analyzing the geometrical phase transition and change in magnetization as the system changes. We estimate the critical temperature for each lattice with blocked region density ρ and found that the critical temperature decreases as the blocked region density increases suggesting that the reduced dimensionality affects the critical behavior for each ρ. Fractal dimension is also measured by determining the cluster size and radius of gyration and using their power-law relation to estimate its value. It is found that general trend of the plot tends towards D = 1 as the density of blocked sites ρ increases, indicating that the dimension is becoming more one-dimensional.