  With the help of the improved Monte Carlo renormalization-group scheme, we
numerically investigate the renormalization group flow of the antiferromagnetic
Heisenberg and XY spin model on the stacked triangular lattice (STA-model) and
its effective Hamiltonian, 2N-component chiral $\phi^4$ model which is used in
the field-theoretical studies. We find that the XY-STA model with the lattice
size $126\times 144 \times 126$ exhibits clear first-order behavior. We also
find that the renormalization-group flow of STA model is well reproduced by the
chiral $\phi^4$ model, and that there are no chiral fixed point of
renormalization-group flow for N=2 and 3 cases. This result indicates that the
Heisenberg-STA model also undergoes first-order transition.
