The influence of non magnetic impurities in the 2d XY model is investigated through Monte Carlo (MC) simulations. The general picture of the transition is fully understood from the Harris criterion which predicts that the universality class is unchanged, and the Berezinskii-Kosterlitz-Thouless description of the topological transition remains valid. We nevertheless address here the question about the influence of dilution on the quasi-long-range order at low temperatures. In particular, we study the asymptotic of the pair correlation function and report the MC estimates for the critical exponent η at different dilutions. In the weak dilution region, our MC calculations are further supported by simple spin-wave-like calculations.

We have performed a massive statistical analysis on the breaking behaviour of Ni nanowires using molecular dynamic simulations. Three stretching directions, five initial nanowire sizes and two temperatures have been studied. We have constructed minimum cross-section histograms and analysed for the first time the role played by monomers and dimers. The shape of such histograms and the absolute number of monomers and dimers strongly depend on the stretching direction and the initial size of the nanowire. In particular, the statistical behaviour of the breakage final stages of narrow nanowires strongly differs from the behaviour obtained for large nanowires. We have analysed the structure around monomers and dimers. Their most probable local configurations differ from those usually appearing in static electron transport calculations. Their non-local environments show disordered regions along the nanowire if the stretching direction is [100] or [110]. Additionally, we have found that, at room temperature, [100] and [110] stretching directions favour the appearance of non-crystalline staggered pentagonal structures. These pentagonal Ni nanowires are reported in this work for the first time. This set of results suggests that experimental Ni conducting histograms could show a strong dependence on the orientation and temperature.

Systems with global symmetry group O(2) experience topological transition in the two-dimensional space. But there is controversy about such a transition for systems with global symmetry group O(3). As an example of the latter case, we study the Lebwohl-Lasher model for the two-dimensional liquid crystal, using three different methods independent of the proper values of possible critical exponents. Namely, we analyze the at-equilibrium order parameter distribution function with (1) the hyperscaling relation; (2) the first-scaling collapse for the probability distribution function; and (3) the Binder's cumulant. We give strong evidence for definite lack of a line of critical points at low temperatures in the Lebwohl-Lasher model, contrary to conclusions of a number of previous numerical studies.

We have constructed computational minimum cross‐section histograms that statistically unveil the presence of preferred configuration during the breakage of Ni nanowires. The computed histograms showed strong dependence on the nanowire stretching direction. For the [100] and [110] stretching directions we have observed a very large peak associated to a minimum cross‐section of 5 atoms. We have confirmed that the configurations that contribute to this peak are staggered pentagonal nanowires. We have found that the formation of these nanowires is enhanced by increasing the temperature up to 550 K. At higher temperatures, the formation of pentagonal nanowires declines due to the competence against the nanowire melting processes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)