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Resolving phase transitions with Discontinuous Galerkin methods

by Eduardo Grossi, Nicolas Wink

Submission summary

As Contributors: Eduardo Grossi · Nicolas Wink
Arxiv Link:
Date submitted: 2019-07-04
Submitted by: Wink, Nicolas
Submitted to: SciPost Physics
Domain(s): Theor. & Comp.
Subject area: High-Energy Physics - Theory


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

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