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Monte Carlo study of the scaling of universal correlation lengths in three-dimensional O(n) spin models

Martin Weigel·Wolfhard Janke
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Abstract

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.

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Martin Weigel, Wolfhard Janke. 2000-07-21. Monte Carlo study of the scaling of universal correlation lengths in three-dimensional O(n) spin models. https://doi.org/10.1103/physrevb.62.6343

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