POTENTIAL FLOW OF THE RENORMALIZATION-GROUP IN A SIMPLE 2-COMPONENT MODEL

The renormalization group (RG) flow on the space of couplings of a sim ple model with two couplings is examined. The model considered is that of a single component scalar field with phi4 self interaction coupled , via Yukawa coupling, to a fermion in flat four-dimensional space. Th e RG flow on the, two-dimensional space of couplings, G, is shown to b e derivable from a potential to sixth order in the couplings, which re quires two-loop calculations of the beta-functions. The identification of a potential requires the introduction of a metric on G and it is s hown that the metric defined by Zamolodchikov, in terms of two-point c orrelation functions of composite operators, gives potential flow to t his order.