Resolving phase transitions with discontinuous Galerkin methods

Abstract:

We demonstrate the applicability and advantages of Discontinuous Galerkin (DG) schemes in the context of the Functional Renormalization Group (fRG). We investigate the $O\left(N\right)$-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.

E. Grossi, N. Wink, „Resolving phase transitions with discontinuous Galerkin methods“, SciPost
Phys. Core 6, 071 (2023).

https://scipost.org/10.21468/SciPostPhysCore.6.4.071

Related to Project B01