  The renormalisation group (RG) flow on the space of couplings of a simple
model with two couplings is examined. The model considered is that of a single
component scalar field with $\phi^4$ self interaction coupled, via Yukawa
coupling, to a fermion in flat four dimensional space. The RG flow on the two
dimensional space of couplings, ${\cal G}$, is shown to be derivable from a
potential to sixth order in the couplings, which requires two loop calculations
of the $\beta$-functions. The identification of a potential requires the
introduction of a metric on ${\cal G}$ and it is shown that the metric defined
by Zamalodchikov, in terms of two point correlation functions of composite
operators, gives potential flow to this order.
