The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group

Details The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group

2011-09-14

arxiv.org/abs/1109.3013v2

J. Phys. A: Math. Theor. 45, 105401 (2012)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 13 figures

Scientific paper

10.1088/1751-8113/45/10/105401

We consider the zero-dimensional O(N) vector model as a simple example to calculate n-point correlation functions using perturbation theory, the large-N expansion, and the functional renormalization group (FRG). Comparing our findings with exact results, we show that perturbation theory breaks down for moderate interactions for all N, as one should expect. While the interaction-induced shift of the free energy and the self-energy are well described by the large-N expansion even for small N, this is not the case for higher-order correlation functions. However, using the FRG in its one-particle irreducible formalism, we see that very few running couplings suffice to get accurate results for arbitrary N in the strong coupling regime, outperforming the large-N expansion for small N. We further remark on how the derivative expansion, a well-known approximation strategy for the FRG, reduces to an exact method for the zero-dimensional O(N) vector model.

Affiliated with

Also associated with

No associations

Rating

The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The zero-dimensional O(N) vector model as a benchmark for perturbation theory, the large-N expansion and the functional renormalization group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-569174