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 dependence in the determination of the universal quantities. We derive new nonperturbative flow equations for the one-component, Z2 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 cut-off employed, the critical exponents become rapidly insensitive to the cut-off width and their values are in good agreement with the results of entirely different approaches.