  We study the flow equation of the O($N$) $\varphi^4$ model in $d$ dimensions
at the next-to-leading order (NLO) in the $1/N$ expansion. Using the
Schwinger-Dyson equation, we derive 2-pt and 4-pt functions of flowed fields.
As the first application of the NLO calculations, we study the running coupling
defined from the connected 4-pt function of flowed fields in the $d+1$
dimensional theory. We show in particular that this running coupling has not
only the UV fixed point but also an IR fixed point (Wilson-Fisher fixed point)
in the 3 dimensional massless scalar theory. As the second application, we
calculate the NLO correction to the induced metric in $d+1$ dimensions with
$d=3$ in the massless limit. While the induced metric describes a 4-dimensional
Euclidean Anti-de-Sitter (AdS) space at the leading order as shown in the
previous paper, the NLO corrections make the space asymptotically AdS only in
UV and IR limits. Remarkably, while the AdS radius does not receive a NLO
correction in the UV limit, the AdS radius decreases at the NLO in the IR
limit, which corresponds to the Wilson-Fisher fixed point in the original
scalar model in 3 dimensions.
