TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.4.071
TI  - Resolving phase transitions with discontinuous Galerkin methods
PY  - 2023/10/25
UR  - https://scipost.org/SciPostPhysCore.6.4.071
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 4
SP  - 071
A1  - Grossi, Eduardo
AU  - Wink, Nicolas
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysCore.6.4.071,
	title={{Resolving phase transitions with discontinuous Galerkin methods}},
	author={Eduardo Grossi and Nicolas Wink},
	journal={SciPost Phys. Core},
	volume={6},
	pages={071},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.4.071},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.4.071},
}