Abstract
Conformal field theory predicts finite-size scaling amplitudes of correlation
lengths universally related to critical exponents on sphere-like, semi-finite
systems Sd − 1×
of arbitrary dimensionality d. Numerical
studies have up to now been unable to validate this result due to the intricacies
of lattice discretisation of such curved spaces. We present a cluster-update Monte
Carlo study of the Ising model on a three-dimensional geometry using slightly
irregular lattices that confirms the validity of a linear amplitude-exponent
relation to high precision.