Finite Callan-Symanzik renormalisation for multiple scalar fields

We study a finite, divergence-free approach to renormalisation originally proposed in the early '70s by Blaer and Young, and Callan. It is based on equations similar to the Callan-Symanzik equations and introduced in the context of the λϕ4 theory. We generalise this method to the case of two interacting scalar fields, with obvious generalisation to an arbitrary number of fields.