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

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.

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

References in corpus (4)

• Improved high-temperature expansion and critical equation of state of three-dimensional Ising-like systems
• High precision Monte Carlo study of the 3D XY-universality class
• The Cluster Processor: New Results
• High-precision determination of the critical exponents for the lambda-transition of 4He by improved high-temperature expansion

Cited by in corpus (4)

• Error estimation and reduction with cross correlations
• Cross-correlations in scaling analyses of phase transitions
• Universal amplitude-exponent relation for the Ising model on sphere-like lattices
• Critical temperatures of the three- and four-state Potts models on the kagome lattice