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

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 S1×S1×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 n⃗ ∞ extrapolation of these simulations against analytical calculations is traced back to a breakdown of the identification of this limit with the spherical model.