Monte Carlo simulation of strongly disordered Ising ferromagnets

We report extensive Monte Carlo simulations of disordered Ising systems in the ferromagnetic region with concentrations of magnetic sites between p=1.0 and 0.5. The magnetization, the susceptibility, and the caloric properties have been studied in the critical region. The critical exponents {β} and {γ} as well as the universal amplitude A of the magnetization and the ratio C₊/C_- of the susceptibility amplitudes have been determined with high precision. In addition to the cusplike specific heat, we have also measured the magnetization-energy correlation function {Γ}, which is a divergent thermal quantity. The corresponding critical exponent {ζ}, which is related to the other exponents by {ζ}=1-{β}=({α}+{γ})/2, has been determined. We have found that all quantities show power-law behavior within the temperature range of our simulation. All critical exponents change continuously with dilution. Even in the range of weak dilution (p{≥}0.8), the effective critical exponents are concentration dependent and are clearly different from their pure system values. In the strongly diluted regime the critical exponents gradually reach new asymptotic behavior at p=0.5--0.6 with values of {β}=0.335±{}0.01 and {γ}=1.49±{}0.02. The exponent {α} of the specific heat becomes -0.17±{}0.04, which corresponds to a cusplike singularity. We conclude that disorder profoundly changes the critical behavior for weakly as well as strongly disordered spin systems.