Numerical extension of CFT amplitude universality to three-dimensional systems

Conformal field theory (CFT) predicts universal relations between scaling amplitudes and scaling dimensions for two-dimensional systems on infinite length cylinders, which hold true even independent of the model under consideration. We discuss different possible generalizations of such laws to three-dimensional geometries. Using a cluster update Monte Carlo algorithm we investigate the finite-size scaling (FSS) of the correlation lengths of several representatives of the class of three-dimensional classical O(n) spin models. We find that, choosing appropriate boundary conditions, the two-dimensional situation can be restored.