Scheme Independence and the Exact Renormalization Group

Abstract

We compute critical exponents in a $Z_2$ symmetric scalar field theory in three dimensions, using Wilson's exact renormalization group equations expanded in powers of derivatives. A nontrivial relation between these exponents is confirmed explicitly at the first two orders in the derivative expansion. At leading order all our results are cutoff independent, while at next-to-leading order they are not, and the determination of critical exponents becomes ambiguous. We discuss the possible ways in which this scheme ambiguity might be resolved.

15 pages, TeX with harvmac, 2 figures in compressed postscript; presentation of first section revised, several minor errors corrected, two references added

References in corpus (3)

• Derivative Expansion of the Exact Renormalization Group
• On Truncations of the Exact Renormalization Group
• Critical Exponents without the Epsilon Expansion

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