6533b7d1fe1ef96bd125d6ab
RESEARCH PRODUCT
Cross Correlations in Scaling Analyses of Phase Transitions
Martin WeigelMartin WeigelWolfhard Jankesubject
Statistical Mechanics (cond-mat.stat-mech)Monte Carlo methodFOS: Physical sciencesGeneral Physics and AstronomyStatistical fluctuationsDynamic Monte Carlo methodMonte Carlo method in statistical physicsStatistical physicsCritical exponentScalingCondensed Matter - Statistical MechanicsImportance samplingMonte Carlo molecular modelingMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-10-11 | Physical Review Letters |