Towards an accurate determination of the critical exponents with the renormalization group flow equations

The determination of the critical exponents by means of the exact renormali zion group approach is still a topic of debate. The general Bow equation is by construction scheme independent, but the use of the truncated derivativ e expansion generates a model dependence in the determination of the univer sal quantities. We derive new nonperturbative flow equations for the one-co mponent, Z(2) symmetric scalar field to the next-to-leading order of the de rivative expansion by means of a class of proper time regulators. The criti cal exponents eta, nu and omega for the Wilson-Fisher fixed point are compu ted by numerical integration of the flow equations, without resorting to po lynomial truncations. We show that by reducing the width of the cut-off emp loyed, the critical exponents become rapidly insensitive to the cut-off wid th and their values are in good agreement with the results of entirely diff erent approaches. (C) 2001 Elsevier Science B.V. All rights reserved.