## SciPost Submission Page

# Resolving phase transitions with Discontinuous Galerkin methods

### by Eduardo Grossi, Nicolas Wink

### Submission summary

As Contributors: | Eduardo Grossi · Nicolas Wink |

Arxiv Link: | https://arxiv.org/abs/1903.09503v3 |

Date submitted: | 2019-07-04 |

Submitted by: | Wink, Nicolas |

Submitted to: | SciPost Physics |

Domain(s): | Theor. & Comp. |

Subject area: | High-Energy Physics - Theory |

### Abstract

We demonstrate the applicability and advantages of Discontinuous Galerkin (DG) schemes in the context of the Functional Renormalization Group (FRG). We investigate the $O(N)$-model in the large $N$ limit. It is shown that the flow equation for the effective potential can be cast into a conservative form. We discuss results for the Riemann problem, as well as initial conditions leading to a first and second order phase transition. In particular, we unravel the mechanism underlying first order phase transitions, based on the formation of a shock in the derivative of the effective potential.

###### Current status:

Editor-in-charge assigned

### List of changes

- Extended explanation of numerical flux

- Slight extension of several other explanations

- Fixed typos

### Submission & Refereeing History

Resubmission 1903.09503v3 on 4 July 2019

Submission 1903.09503v2 on 24 April 2019