Towards an accurate determination of the critical exponents with the Renormalization Group flow equations

Bonanno, A, Zappalà, D

Published Jan 1, 2001• 62 citations

Abstract

The determination of the critical exponents by means of the Exact Renormalizion Group approach is still a topic of debate. The general flow equation is by construction scheme independent, but the use of the truncated derivative expansion generates a model depencence in the determination of the universal quantities. We derive new nonperturbative flow equations for the one-component, Z_2 symmetric scalar field to the next-to-leading order of the derivative expansion by means of a class of proper time regulators. The critical exponents eta, nu and omega for the Wilson-Fisher fixed point are computed by numerical integration of the flow equations, without resorting to polynomial truncations. We show that by reducing the width of the cut-off employed, the critical exponents become rapidly insensitive to the cut-off width and converge to values that are in good agreement with the results of entirely different approaches.

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