  We study the 3d Ising universality class using the functional renormalisation
group. With the help of background fields and a derivative expansion up to
fourth order we compute the leading index, the subleading symmetric and
anti-symmetric corrections to scaling, the anomalous dimension, the scaling
solution, and the eigenperturbations at criticality. We also study the
cross-correlations of scaling exponents, and their dependence on
dimensionality. We find a very good numerical convergence of the derivative
expansion, also in comparison with earlier findings. Evaluating the data from
all functional renormalisation group studies to date, we estimate the
systematic error which is found to be small and in good agreement with findings
from Monte Carlo simulations, \epsilon-expansion techniques, and resummed
perturbation theory.
