# Resolving phase transitions with Discontinuous Galerkin methods

### Submission summary

 As Contributors: Eduardo Grossi · Nicolas Wink Arxiv Link: https://arxiv.org/abs/1903.09503v2 Date submitted: 2019-04-24 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

### Submission & Refereeing History

Submission 1903.09503v2 on 24 April 2019