Nonsingular increase in magnetic susceptibility and transition in universality in site-diluted Ising model in two dimensions

Abstract

We study the effects of dilution to the critical properties of site-diluted Ising model in two dimensions using Monte Carlo simulations. Quenched disorder from the dilution is incorporated into the Ising model via random empty sites on the square lattice of Ising spins. Thermodynamic quantities such as the magnetization $M$ per spin, energy $E$ per spin, magnetic susceptibility $χ$ per spin, and specific heat $C$ per spin are then calculated after the system has equilibrated. At small dilution concentrations $d<0.1$, we find that the value of the critical exponent $β$ does not deviate from its pure Ising value. At higher dilution concentrations $d>0.1$, however, we find $β$ to strongly depend on the value of $d$. We are able to locate a critical temperature $T_c$ and a critical dilution concentration $d_c$ where the phase transition occurs. We find $T_c$ to depend linearly on $d$. In the phase diagrams of $M$, $E$, $χ$, and $C$, we find that the phase transition line eventually disappears at high dilutions. Our results suggest that there is a transition from Strong Universality at low dilution to Weak Universality at high dilution. Lastly, we find a wide and nonsingular increase in the magnetic susceptibility $χ$ at the low temperature and high dilution region.