  Fixed-point equations in the functional renormalization group approach are
integrated from large to vanishing field, where an asymptotic potential in the
limit of large field is implemented as initial conditions. This approach allows
us to obtain a global fixed-point potential with high numerical accuracy, that
incorporates the correct asymptotic behavior in the limit of large field. Our
calculated global potential is in good agreement with the Taylor expansion in
the region of small field, and it also coincides with the Laurent expansion in
the regime of large field. Laurent expansion of the potential in the limit of
large field for general case, that the spatial dimension $d$ is a continuous
variable in the range $2\leq d \leq 4$, is obtained. Eigenfunctions and
eigenvalues of perturbations near the Wilson-Fisher fixed point are computed
with the method of eigenperturbations. Critical exponents for different values
of $d$ and $N$ of the $O(N)$ universality class are calculated.
