  We calculate the two-loop renormalization group (RG) beta-function of a
massless scalar field theory from the irreducible version of Polchinski's exact
RG flow equation. To obtain the correct two-loop result within this method, it
is necessary to take the full momentum-dependence of the irreducible four-point
vertex and the six-point vertex into account. Although the same calculation
within the orthodox field theory method is less tedious, the flow equation
method makes no assumptions about the renormalizability of the theory, and
promises to be useful for performing two-loop calculations for
non-renormalizable condensed-matter systems. We pay particular attention to the
problem of the field rescaling and the effect of the associated exponent eta on
the RG flow.
