## 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 {eta}. 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). ((orig.)).

## Citation Formats

Morris, T R.
The derivative expansion of the renormalization group.
Netherlands: N. p.,
1995.
Web.
doi:10.1016/0920-5632(95)00389-Q.

Morris, T R.
The derivative expansion of the renormalization group.
Netherlands.
doi:10.1016/0920-5632(95)00389-Q.

Morris, T R.
1995.
"The derivative expansion of the renormalization group."
Netherlands.
doi:10.1016/0920-5632(95)00389-Q.
https://www.osti.gov/servlets/purl/10.1016/0920-5632(95)00389-Q.

@misc{etde_101045,

title = {The derivative expansion of the renormalization group}

author = {Morris, T R}

abstractNote = {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 {eta}. 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). ((orig.)).}

doi = {10.1016/0920-5632(95)00389-Q}

journal = {Nuclear Physics B, Proceedings Supplements}

volume = {42}

journal type = {AC}

place = {Netherlands}

year = {1995}

month = {Apr}

}

title = {The derivative expansion of the renormalization group}

author = {Morris, T R}

abstractNote = {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 {eta}. 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). ((orig.)).}

doi = {10.1016/0920-5632(95)00389-Q}

journal = {Nuclear Physics B, Proceedings Supplements}

volume = {42}

journal type = {AC}

place = {Netherlands}

year = {1995}

month = {Apr}

}