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
Tc and a critical dilution concentration
dc where the phase transition occurs. We find
Tc 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.
In this work, we simulated a quenched random mixed-spin Ising model on the square lattice. The model system consists of two different particles with spins σ = 1/2 (states ±1/2) and S = 1 (states ±1, 0). These particles are randomly distributed on the lattice, and we considered only nearest-neighbor interactions. This model can represent a random magnetic binary alloy AxB1-x, obtained from the high-temperature quenching of a liquid mixture. We performed Monte Carlo simulations for several lattice sizes and temperatures, and we found its critical temperature through the reduced fourth-order cumulant. We also determined the magnetization, the susceptibility, and the specific heat as a function of temperature. We used finite-size scaling arguments to estimate the critical exponents β, γ, and ν of the model. We showed that the quenched model is in the same universality class of the two-dimensional pure Ising model. We also investigated the sample to sample fluctuations that occur in the values of the thermodynamic quantities in order to describe the self-averaging properties at the critical point.
The two-dimensional random bond Ising model with two distinct ferromagnetic nearest-neighbour couplings, J and J ', distributed randomly over the lattice with concentration 1/2 is studied for various ratios J '/ J at criticality. The critical temperature is exactly known from self-duality. The size-dependent specific heat shows a crossover from the perfect Ising to the randomness-dominated critical behaviour of doubly logarithmic form. In the latter region, our estimates for the critical exponents of the size-dependent magnetization and susceptibility are in very good agreement with analytic results suggesting β/ν = 1/8 and γ/ν = 7/4.