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

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

2000-03-08

arxiv.org/abs/cond-mat/0003124v2

Phys.Rev.B62:6343-6359,2000

Physics

Condensed Matter

Statistical Mechanics

18 pages, 9 figures, REVTeX4, slightly shortened, updated critical exponent estimates

Scientific paper

10.1103/PhysRevB.62.6343

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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