### Abstract

The concept of conformal field theory provides a general classification of statistical
systems on two-dimensional geometries at the point of a continuous phase transition.
Considering the finite-size scaling of certain special observables, one thus obtains not only
the critical exponents but even the corresponding amplitudes of the divergences analytically.
A first numerical analysis brought up the question whether analogous results can be obtained
for those systems on three-dimensional manifolds.
Using Monte Carlo simulations based on the Wolff single-cluster update algorithm we investigate
the scaling properties of O(n) symmetric classical spin models on a three-dimensional,
hyper-cylindrical geometry with a toroidal cross-section considering both periodic and antiperiodic
boundary conditions. Studying the correlation lengths of the Ising, the XY, and
the Heisenberg model, we find strong evidence for a scaling relation analogous to the twodimensional
case, but in contrast here for the systems with antiperiodic boundary conditions.

Original language | English |
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Pages (from-to) | 575-579 |

Journal | Annalen der Physik |

Volume | 7 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - Nov 1998 |

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### Bibliographical note

The full text is not available on the repository.### Keywords

- Spin models
- Finite-size scaling
- Universal amplitudes
- Conformal field theory