  We study the critical properties of the spin-continuous $S^{4}$ system on the
typical translational invariant triangular lattices by combining the
recently-developed generalized Migdal-Kadanoff bond-moving recursion procedures
with the cumulative expansion technique. In three different cases of
nearest-neighbor, next nearest neighbor and external field we obtain the
critical points and further calculate the critical exponents according to the
scaling theory. In all case it is found that there exists three fixed points.
The correlation length critical exponents obtained near the Wilson-Fisher fixed
points are found getting smaller and smaller with the increasing of the system
complexity. Others are found similar to the results of the classical Gaussian
model and different from those of the Ising system.
