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

A. Bonanno·D. Zappalà
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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 dependence 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 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.

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A. Bonanno, D. Zappalà. 2000-12-23. Towards an accurate determination of the critical exponents with the Renormalization Group flow equations. https://doi.org/10.1016/s0370-2693(01)00273-8

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