  We study scalar conformal field theories whose large $N$ spectrum is fixed by
the operator dimensions of either Ising model or Lee-Yang edge singularity.
Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find
a series of kinks whose locations approach
$(\Delta^{\text{Ising}}_{\sigma},\Delta^{\text{Ising}}_{\epsilon})$ at
$N\rightarrow \infty$. Setting $N=4$, we study the cubic anisotropic fixed
point with three spin components. As byproducts of our numerical bootstrap
work, we discover another series of kinks whose identification with previous
known CFTs remains a mystery. We also show that "minimal models" of
$\mathcal{W}_3$ algebra saturate the numerical bootstrap bounds of CFTs with
$S_3$ symmetry.
