In this work, we evaluate the probability distribution function of the order parameter for the two-dimensional site-diluted Ising model. Extensive Monte Carlo simulations have been performed for different spin concentrations p (0.70

In this work we apply a highly efficient Monte Carlo algorithm recently proposed by Newman and Ziff to treat percolation problems. The site and bond percolations are studied on a number of lattices in two and three dimensions. Quite good results for the wrapping probabilities, correlation length critical exponent, and critical concentration are obtained for the square, simple cubic, hexagonal close packed, and hexagonal lattices by using relatively small systems. We also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution.

Advanced chain-growth computer simulation methodologies have been employed for a systematic statistical analysis of the critical behavior of a polymer adsorbing at a substrate. We use finitesize scaling techniques to investigate the solvent-quality dependence of critical exponents, critical temperature, and the structure of the phase diagram. Our study covers all solvent effects from the limit of super-self-avoiding walks, characterized by effective monomer-monomer repulsion, to poor solvent conditions that enable the formation of compact polymer structures. The results significantly benefit from taking into account corrections to scaling.

We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin magnetic systems on a lattice, such as Ising, general spin-S Blume-Capel and Baxter-Wu, Q-state Potts, among other models, will be considered as examples. The importance and the necessity of the role of mixing fields in asymmetric magnetic models will be discussed in more detail, as well as the corresponding distributions of the extensive conjugate variables.