Cross correlations in scaling analyses of phase transitions

Martin Weigel, W. Janke

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Abstract

Thermal or finite-size scaling analyses of importance sampling Monte Carlo computer simulations 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 often results in 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.
Original languageEnglish
Article number100601
JournalPhysical Review Letters
Volume102
Issue number10
DOIs
Publication statusPublished - 2009

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cross correlation
scaling
estimates
transition points
estimators
computerized simulation
sampling
exponents
costs

Bibliographical note

© 2009 American Physical Society

Keywords

  • scaling analyses
  • phase transitions

Cite this

Cross correlations in scaling analyses of phase transitions. / Weigel, Martin; Janke, W.

In: Physical Review Letters, Vol. 102, No. 10, 100601, 2009.

Research output: Contribution to journalArticle

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