DiFfRG: A discretisation framework for functional renormalisation group flows
- 1Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120, Heidelberg, Germany
- 2ExtreMe Matter Institute EMMI, GSI, Planckstr. 1, 64291, Darmstadt, Germany
Abstract
We introduce DiFfRG ( Di scretisation F ramework for f unctional R enormalisation G roup flows), a comprehensive computational C++ framework for solving functional Renormalisation Group flows in very general truncation schemes. Its central features are threefold: Firstly, the use of Finite Element Methods (FEM) for efficient, easy to set up and quantitatively reliable computation of field dependences. Secondly, the (simultaneous) setup of large, fully momentum-dependent vertex expansions. Thirdly, efficient time-discretisation methods incorporating insights from studies of solving theories which exhibit spontaneous symmetry breaking, going hand in hand with shocks and an exponential increase of the information flow velocity in field space. The framework provides a Mathematica package for automatic code generation of flow equations, finite and zero temperature integration routines with support for GPU hardware and extensive parallelisation capabilities. Detailed examples and tutorials are provided and discussed herein which showcase and introduce the framework to the user. We illustrate the capabilities of DiFfRG with four examples, with the complete codes fully included: finite temperature O(N) theory, a Quark-Meson model, SU(3) Yang-Mills theory and four-Fermi flows in the QCD phase diagram. PROGRAM SUMMARY Program Title: DiFfRG Licensing provisions: GPLv3 Programming language: C++, Mathematica, Python Computer: Any Linux/Mac machine Nature of problem: Evaluate large systems of fRG flows with full effective potentials and/or vertex expansions Solution method: Combine finite element methods and efficient time-steppers with fast numerical integration of flow equations and momentum grids. Unusual features: The code-generation capabilities of the Mathematica subpackage allow for very fast development of extremly large systems of flow equations. Field-space discretisations can be easily defined by the user with a range of different finite element methods.
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BibTeX
@article{sattler2026diffrg,
title = {{DiFfRG: A discretisation framework for functional renormalisation group flows}},
author = {Franz R. Sattler and Jan Martin Pawlowski},
journal = {Computer Physics Communications},
year = {2026},
month = jun,
doi = {10.1016/j.cpc.2026.110262},
url = {https://doi.org/10.1016/j.cpc.2026.110262},
note = {CC BY},
}
RIS
TY - JOUR
TI - DiFfRG: A discretisation framework for functional renormalisation group flows
AU - Franz R. Sattler
AU - Jan Martin Pawlowski
PY - 2026
DA - 2026/06/25
JO - Computer Physics Communications
DO - 10.1016/j.cpc.2026.110262
UR - https://doi.org/10.1016/j.cpc.2026.110262
AB - We introduce DiFfRG ( Di scretisation F ramework for f unctional R enormalisation G roup flows), a comprehensive computational C++ framework for solving functional Renormalisation Group flows in very general truncation schemes. Its central features are threefold: Firstly, the use of Finite Element Methods (FEM) for efficient, easy to set up and quantitatively reliable computation of field dependences. Secondly, the (simultaneous) setup of large, fully momentum-dependent vertex expansions. Thirdly, efficient time-discretisation methods incorporating insights from studies of solving theories which exhibit spontaneous symmetry breaking, going hand in hand with shocks and an exponential increase of the information flow velocity in field space. The framework provides a Mathematica package for automatic code generation of flow equations, finite and zero temperature integration routines with support for GPU hardware and extensive parallelisation capabilities. Detailed examples and tutorials are provided and discussed herein which showcase and introduce the framework to the user. We illustrate the capabilities of DiFfRG with four examples, with the complete codes fully included: finite temperature O(N) theory, a Quark-Meson model, SU(3) Yang-Mills theory and four-Fermi flows in the QCD phase diagram. PROGRAM SUMMARY Program Title: DiFfRG Licensing provisions: GPLv3 Programming language: C++, Mathematica, Python Computer: Any Linux/Mac machine Nature of problem: Evaluate large systems of fRG flows with full effective potentials and/or vertex expansions Solution method: Combine finite element methods and efficient time-steppers with fast numerical integration of flow equations and momentum grids. Unusual features: The code-generation capabilities of the Mathematica subpackage allow for very fast development of extremly large systems of flow equations. Field-space discretisations can be easily defined by the user with a range of different finite element methods.
SN - 0010-4655
SN - 1879-2944
ER -