Do the terms "basin of attraction of fixed point" and "critical surfaces" denote the same thing? Critical surfaces are defined as infinite-dimensional surfaces on the space of theories on which the mass gap vanishes, and consequently the correlation lengths blow up.
However Kardar defines basin of attraction of fixed point as the subspace spanned by irrelevant couplings about the fixed point, and further shows that the correlation lengths blow up there.
I am confused here, do these two surfaces denote the same thing, or are there examples where the basin of attraction of the RG flow and critical surfaces are different?
 A: The technical name for "basin of attraction" in the theory of dynamical systems (like the RG) is stable manifold of a fixed point. In 3d for a scalar field/Ising model, just looking at the $\mathbb{Z}_2$ even sector, and ignoring the $(\partial\phi)^2$ marginal direction, the critical surface $C$ defined by infinite correlation length should be a codimension one submanifold in the space of theories $T$. There should be two fixed points Gaussian one $P_G$ and the Wilson-Fisher fixed point $P_{WF}$. The stable manifold of $P_{WF}$ should be $C\backslash\{P_G\}$.
In 2d however the situation is more complicated because there infinitely many fixed points $P_4,P_6,P_8,\ldots$ corresponding to interactions $\phi^{4}, \phi^{6},\phi^{8}, \ldots$
$P_4$ is basically $P_{WF}$. The stable manifolds of these fixed points gets smaller with the interaction exponent, or rather their codimension increases. There is a trajectory going from $P_k$ to $P_{k-2}$, see for instance https://arxiv.org/abs/0907.2560 and references therein.
