Extending the Gaussian model by introducing a second field and coupling it to the other field, I consider the Hamiltonian
$$\beta H = \frac{1}{(2\pi)^d} \int_0^\Lambda d^d q \frac{t + Kq^2}{2} |m(q)|^2 + \frac{L}{2} q^4 |\phi|^2 + v q^2 m(q) \phi^*(q)$$
Doing a Renormalization Group treatment, I integrate out the high wave-numbers above $\Lambda/b$ and obtain the following recursion relations for the parameters: $$\begin{aligned}t' &= b^{-d} z^2 t & K' &= b^{-d-2}z^2 K & L' &= b^{-d-4}y^2 L \\ v' &= b^{-d-2}yz v & h' &= zh \end{aligned}$$ where $z$ is the scaling of field $m$ and $y$ is the scaling of field $\phi$.
One way to obtain the scaling factors $z$ and $y$ is to demand that $K' = K$ and $L' = L$, i.e., we demand that fluctuations are scale invariant.
But apparently, there is another fixed point if we demand that $t' = t$ and $L' = L$ which gives rise to different scaling behavior, and I wonder
a) why I can apparently choose which parameters should be fixed regardless of their value ($K$ and $L$ in one case, $t$ and $L$ in the other case)
b) what the physical meaning of these two different fixed points is...
(My exposure to field theory/RG is from a statistical physics approach, so if answers could be phrased in that language as opposed to QFT that'd be much appreciated)
