  In this work we re-examine the Wilson Fisher fixed point. We study Wilsonian
momentum space renormalization group (RG) flow for various forms of the cutoff.
We show that already at order $\left(4-d\right)^{1}$, where $d$ is the
dimension of the $\phi^{4}$ theory, there are changes to the position of the
fixed point and the direction of irrelevant coupling parameters. We also show
in a multi-flavor $\phi^{4}$ model that symmetries of the Lagrange function can
be destroyed if the different flavors have different cutoffs (that is the
Lagrangian can flow to a non-symmetric fixed point). Some related comments are
made about a similar situation in parquet RG (pRG). In future works we will
study Wilsonian RG to order $\left(4-d\right)^{2}$ and find non-universal
critical exponents that depend on the cutoff.
