Search results for "Statistical fluctuations"
showing 2 items of 12 documents
Cross Correlations in Scaling Analyses of Phase Transitions
2008
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to reduce statistical fluctuations. We point out that the origin of such estimates in the same time series results in often pronounced cross-correlations which are usually ignored even in high-precision studies, generically leading to significant underestimation of statistical fluctuations. We suggest to use a simple extension of the conventional analysis taking correlation effects into account, which leads to improved estimators with often substantially reduced …
Classical Statistical Mechanics
2003
Some aspects of statistical mechanics that are particularly important for computer simulation approaches are recalled. Using Ising and classical Heisenberg models as examples, various statistical ensembles and appropriate thermodynamic potentials are introduced, and concepts such as Legendre transformations between ensembles and the thermodynamic integration method to obtain the entropy are mentioned. Probability distributions characterizing statistical fluctuations are discussed, fluctuation relations for response functions are derived, and the behavior of these quantities at first and second order phase transitions are described qualitatively. Also the general consequences of phase coexis…