The effective potential and the renormalisation group

We discuss renormalisation group improvement of the effective potential both in general and in the context of $O(N)$ scalar ${\text{p}}^4$ and the Standard Model. In the latter case we find that absolute stability of the electroweak vacuum implies that $m_H\ge 1.95m_t-189GeV$, for $\text{as}(M_Z)=0.11$. We point out that the lower bound on $m_H$ {\it decreases/} if $\text{as}(M_Z)$ is increased.