Dresden 2009 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 6: Critical phenomena and phase transitions
DY 6.4: Talk
Monday, March 23, 2009, 15:30–15:45, ZEU 118
Cross-correlations in scaling analyses of phase transitions — •Martin Weigel1 and Wolfhard Janke2 — 1Institut für Physik, KOMET 331, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany — 2Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100 920, D-04009 Leipzig, Germany
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 statistical fluctuations at almost no extra cost in terms of computation time.