Two-loop β-function from the exact renormalization group

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 how 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 n on the RG now. (C) 2001 Elsevier Science B.V. All rights reserved.