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Four Loop Scalar ϕ^{4} Theory Using the Functional Renormalization Group^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Notation

## 3. Flow Equations

## 4. Numerical Method

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The physical vertex $V\left(0\right)$ versus ${p}_{\mathrm{max}}$ with $\lambda =2$, $T=2$ and $L=4$ at 4 loop level in the skeleton expansion. To set the scale we also show the results of an incorrect calculation (see text for more explanation).

**Figure 2.**The pressure as a function of coupling. The right panel shows a close up of the large coupling region where the three approximations start to diverge from each other.

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**MDPI and ACS Style**

Carrington, M.E.; Phillips, C.D.
Four Loop Scalar *ϕ*^{4} Theory Using the Functional Renormalization Group. *Universe* **2019**, *5*, 9.
https://doi.org/10.3390/universe5010009

**AMA Style**

Carrington ME, Phillips CD.
Four Loop Scalar *ϕ*^{4} Theory Using the Functional Renormalization Group. *Universe*. 2019; 5(1):9.
https://doi.org/10.3390/universe5010009

**Chicago/Turabian Style**

Carrington, Margaret E., and Christopher D. Phillips.
2019. "Four Loop Scalar *ϕ*^{4} Theory Using the Functional Renormalization Group" *Universe* 5, no. 1: 9.
https://doi.org/10.3390/universe5010009