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.)).
Morris, T R
[1]
- Southampton Univ. (United Kingdom). Dept. of Physics
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.
https://doi.org/10.1016/0920-5632(95)00389-Q
Morris, T R.
1995.
"The derivative expansion of the renormalization group."
Netherlands.
https://doi.org/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 = []
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 = []
volume = {42}
journal type = {AC}
place = {Netherlands}
year = {1995}
month = {Apr}
}