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 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 η, ν and ω 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 cutoff employed, the critical exponents become rapidly insensitive to the cutoff width and converge to values that are in good agreement with the results of entirely different approaches.