The Wikipedia page on quantum triviality seems to give two different definitions for the term that are not obviously equivalent.
Some parts of the page seem to define a renormalizable theory as "quantum trivial" if it has a Landau pole. In other words, if you "run the renormalization group backwards" into the UV, you find that the strength of the coupling constant diverges at a finite energy scale. (The physical significance of this process is dubious, because (a) we can't actually calculate the RG flow in practice when the coupling is strong, and (b) the RG flow is not actually reversible, as higher-mass fields that the original theory cannot predict might become important at higher energy scales.) This definition defines "quantum triviality" in terms of the theory's UV behavior.
Other parts of the page seem to define a renormalizable theory as "quantum trivial" if its IR fixed point is free. In condensed-matter terminology (which tends to only consider IR behavior, due to the atomic lattice's modifying the field theory at modest energy scales), this means that all of the interactions are marginally irrelevant. This definition defines "quantum triviality" in terms of the theory's IR behavior.
At the one-loop level, these two definitions are equivalent: they both amount to the coefficient of the leading-order term in the beta function being positive. But are they equivalent in general? It seems logically possible to me that the exact function $g(\mu/\mu_0)$ could either (a) diverge at some $\mu/\mu_0 > 1$ but satisfy $g(\mu = 0) > 0$, which would satisfy the first definition of "quantum triviality" but not the second, or else (b) have $g(\mu = 0) = 0$ but remain finite at all $\mu$, which would satisfy the second definition but not the first.
If these definitions are not equivalent, then is either one more standard in the physics community?