We study the phase diagram of the site-diluted Ising model in a wide dilution range, through Monte Carlo simulations and finite-size scaling techniques. Our results for the critical exponents and universal cumulants turn out to be dilution independent, but only after a proper infinite volume extrapolation, taking into account the leading corrections-to-scaling terms. ͓S0163-1829͑98͒00429-9͔

We have simulated, using parallel tempering, the three-dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (Lϭ20) has been studied using a dedicated computer ͑the SUE machine͒. We have obtained, measuring the correlation length in the critical region, strong evidence for a second-order finite-temperature phase transition, ruling out other possible scenarios like a KosterlitzThouless phase transition. Precise values for the and critical exponents are also presented.

We study the critical properties of three-dimensional O(N ) models, for N = 2, 3, 4. Parameterizing the leading corrections-to-scaling for the η exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte Carlo values, but in agreement with ǫ-expansions. We also measure the critical exponent related with the tensorial magnetization as well as the ν exponents and critical couplings.

Using Finite-Size Scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention in parameterizing the corrections-to-scaling, what is necessary to put the systematic errors below the statistical ones.

We present the results of a Monte Carlo simulation of the RP 2 model in three dimensions with negative coupling. We observe a second order phase transition between the disordered phase and an antiferromagnetic, unfrustrated, ordered one. We measure, with a Finite Size Scaling analysis, the thermal exponent, obtaining ν = 0.784(8). We have found two magnetic-type relevant operators whose related η exponents are 0.038(2) and 1.338(8) respectively.