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DiFfRG: A discretisation framework for functional renormalisation group flows
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DOI：10.1016/j.cpc.2026.110262.png)
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Abstract
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We introduce DiFfRG (Discretisation Framework for functional Renormalisation Group 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.
Keywords:
Functional renormalization group
Numerical hydrodynamics
Automatic code generation
High energy physics
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