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Using the newly proposed probability-changing cluster (PCC) Monte Carloalgorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Sincewe can tune the critical point of each random sample automatically with the PCCalgorithm, we succeed in studying the sample-dependent $T_c(L)$ and the sampleaverage of physical quantities at each $T_c(L)$ systematically. Using thefinite-size scaling (FSS) analysis for $T_c(L)$, we discuss the importance ofcorrections to FSS both in the strong-dilution and weak-dilution regions. Thecritical phenomena of the 2D site-diluted Ising model are shown to becontrolled by the pure fixed point. The crossover from the percolation fixedpoint to the pure Ising fixed point with the system size is explicitlydemonstrated by the study of the Binder parameter. We also study thedistribution of critical temperature $T_c(L)$. Its variance shows the power-law$L$ dependence, $L^{-n}$, and the estimate of the exponent $n$ is consistentwith the prediction of Aharony and Harris [Phys. Rev. Lett. {\bf 77}, 3700(1996)]. Calculating the relative variance of critical magnetization at thesample-dependent $T_c(L)$, we show that the 2D site-diluted Ising modelexhibits weak self-averaging.Comment: 6 pages including 6 eps figures, RevTeX, to appear in Phys. Rev.

Crossover and self-averaging in the two-dimensional site-diluted Ising model: Application of probability-changing cluster algorithm