How fractal defects can affect critical phenomena?

Abstract

We investigate the two-dimensional Ising model with fractal defects using Monte Carlo simulations. The defects are constructed in the form of a diffusion-limited aggregation shape. Our findings indicate that the presence of fractal defects does not change the critical temperatures across different defect concentrations. However, through an analysis of short-time dynamics, we observe that both the critical equilibrium exponents $\beta$, $\nu$ and $\gamma$, as well as the dynamical exponents $z$ and $\theta$, exhibit a strong dependence on the defect size concentration $P$. This suggests that the fractal defects alter the universality class of the system.