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arXiv · hep-lat/9411053

The derivative expansion of the renormalization group

Tim R. Morris
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Abstract

By writing the flow equations for the continuum Legendre effective action (a.k.a. Helmholtz free energy) with respect to a particular form of smooth cutoff, and performing a derivative expansion up to some maximum order, a set of differential equations are obtained which at FPs (Fixed Points) reduce to non-linear eigenvalue equations for the anomalous scaling dimension $η$. Illustrating this by expanding (single component) scalar field theory, in two, three and four dimensions, up to second order in derivatives, we show that the method is a powerful and robust means of discovering and quantifying non-perturbative continuum limits (continuous phase transitions).

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Tim R. Morris. 1994-11-25. The derivative expansion of the renormalization group. https://doi.org/10.1016/0920-5632(95)00389-q

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