Numerical tests of conjectures of conformal field theory for three-dimensional systems
arXiv:cond-mat/9904091 · doi:10.1002/(SICI)1521-3889(199811)7:5/6<575::AID-ANDP575>3.0.CO;2-M
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 two-dimensional case, but in contrast here for the systems with antiperiodic boundary conditions.
4 pages, LaTeX, proceedings of the 210th WE-Heraeus Seminar PILS'98, Berlin