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Comment: 5 pages, 4 figures, elsarticle
The importance-sampling Monte Carlo algorithm appears to be the universally optimal solution to the problem of sampling the state space of statistical mechanical systems according to the relative importance of configurations for the partition function or thermal averages of interest. While this is true in terms of its simplicity and universal applicability, the resulting approach suffers from the presence of temporal correlations of successive samples naturally implied by the Markov chain underlying the importance-sampling simulation. In many situations, these autocorrelations are moderate and can be easily accounted for by an appropriately adapted analysis of simulation data. They turn out to be a major hurdle, however, in the vicinity of phase transitions or for systems with complex free-energy landscapes. The critical slowing down...
Comment: 28 pages, 15 figures, 2 tables, version as published
Comment: 15 pages, 14 figures, one table, submitted to PRE
Comment: 4 pages, RevTEX4, 3 tables, 1 figure
Comment: 16 pages, RevTEX4, 4 figures, 6 tables, published version
Comment: to appear in Eur. Phys. J. Spec. Top. issue "Computer simulations on GPU"
Using an elaborate set of simulational tools and statistically optimized methods of data analysis we investigate the scaling behavior of the correlation lengths of three-dimensional classical O($n$) spin models. Considering three-dimensional slabs $S^1\times S^1\times\mathbb{R}$, the results over a wide range of $n$ indicate the validity of special scaling relations involving universal amplitude ratios that are analogous to results of conformal field theory for two-dimensional systems. A striking mismatch of the $n\to\infty$ extrapolation of these simulations against analytical calculations is traced back to a breakdown of the identification of this limit with the spherical model.
Comment: 6 pages, 2 figures, Europhys. Lett., in print
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