Numerical extension of CFT amplitude universality to three-dimensional systems

Conformal field theory (CFT) predicts universal relations between scaling a mplitudes and scaling dimensions for two-dimensional systems on infinite le ngth cylinders, which hold true even independent of the model under conside ration. We discuss different possible generalizations of such laws to three -dimensional geometries. Using a cluster update Monte Carlo algorithm we in vestigate the finite-size scaling (FSS) of the correlation lengths of sever al representatives of the class of three-dimensional classical O(n) spin mo dels. We find that, choosing appropriate boundary conditions, the two-dimen sional situation can be restored. O 2000 Elsevier Science B.V. All rights r eserved.