Fractal dimension, critical exponents, and weak universality on a modified 2D Ising model


We investigate the behavior of a 2D square Ising system with central regions without spins, providing insights into its critical behavior and dimensionality. Increasing the density of these regions changes the dimensionality of the finite lattice, and the critical temperature decreases as the blocked region density increases, consistent with a similar percolation study in 2D. The fractal dimension tends towards D = 1 as the density of blocked sites increases, indicating a more one-dimensional lattice system. Results from the analysis of modified Ising system, where the value of β varies with the degree of dilution or the density of blocked region, ρ, supports the weak universality hypothesis.