Global Wilson–Fisher fixed points

The Wilson–Fisher fixed point with O(N) universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed points to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantities such as scaling exponents and mass ratios are computed, for all N , together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite- N results do not converge pointwise towards the exact infinite- N limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated