Numerical Tests of Conjectures of Conformal Field Theory for Three-Dimensional Systems

Martin Weigel, W. Janke

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)575-579
JournalAnnalen der Physik
Volume7
Issue number5-6
DOIs
Publication statusPublished - Nov 1998

    Fingerprint

Bibliographical note

The full text is not available on the repository.

Keywords

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

Cite this