Fenômenos críticos em gases de rede - Antonio Goncalves da Cunha Neto (2012)
Critical properties of lattice gases with nearest-neighbor exclusion (NNE) are investigated via adaptive-window Wang-Landau sampling (WLS) on the square and simple cubic lattices, for which the model is known to exhibit an Ising-like phase transition. We study the particle density, order parameter, compressibility, Binder cumulant and susceptibility, in efforts to test WLS, which has been used quite widely in recent years, in the context of lattice gaes. Of considerable interest is whether it is possible to estimate critical exponents reliably using WLS with adaptive windows. We find that method yields results in fair agreement with values (in two dimensions) and numerical estimates (in three dimensions). In the next study using WLS, we investigate entropic demixing in a two-dimensional binary lattice-gas mixture. The system consists of large particles which exclude occupation of nearest neighbor-sites and small particles with on-site exclusion only. We study the critical properties of the system and compare our results with exact enumerations and with the case when Zs= 0, i.e, the NNW lattice gas. The phase diagram of the model ir obtained through Monte Carlo simulation for lattice sizes up 48x48. The diagram in the density-plane is used to obtain the densities at tricritical point as pl,t= 0,2029 (1) and ps,t= 0,318 (2). We stress that WLS permits the avaliation of the number of configurations, restricting the sample over onde window. We observe that attempts to restrict the sampling to a subset of the full energy range lead to distortions in the density of states. It limits the evaluation of the density of states for larger system, necessary to contour finite size effects. To avoid this disadvantage we propose a new Monte Carlo technique. We introduce tomographic entropic sampling, a scheme which uses multiple studies, starting from different regions of configuration space, to yield precise estimates of the number of configurations over the full range of energies, without dividing the latter into subsets or windows. Applied to the Ising model on the square lattice, the method yields the critical temperature to an accuracy of about 0,01%, and critical exponents to 0.5% or better. Predictions for systems sizes L= 10-160, for the temperature of the specific heat maximum, and the specific heat at the critical temperature, are in very close agreement with exact results. For the Ising model on the simple cubic lattice the critical temperature is given to within 0,004% of the best avaible estimates, using results for system sizes 8-32; the exponent ratios â/í and /í are given to within about 3% and 1%, respectively, of the best avaible estimates. In both two and three dimensions, results for the antiferromagnetic critical point are fully consistent with those of the ferromagnetic transition. Application to the lattice gas with nearest-neighbor exclusion on the square lattice again yields the critical chemical potential and exponent ratios â/í and /í to good precision.