  The solvability of the three-dimensional O($N$) scalar field theory in the
large $N$ limit makes it an ideal toy model exhibiting "walking" behavior,
expected in some SU($N$) gauge theories with a large number of fermion flavors.
We study the model using lattice regularization and show that when the ratio of
the particle mass to an effective 4-point coupling (with dimension mass) is
small, the beta function associated to the running 4-point coupling is
"walking". We also study lattice artifacts and finite size effects, and find
that while the former can be sizable at realistic correlation length, the
latter are under control already at lattice sizes a few ($\sim$3) correlation
lengths. We show the robustness of the walking phenomenon by showing that it
can also be observed by studying physical observables such as the scattering
phase shifts and the mass gap in finite volume.
