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Lattice Monte Carlo meets the lattice functional renormalization group: A quantitative comparison

Niklas Zorbach1,*, Jan Philipp Klinger2,†, Owe Philipsen2,‡, and Jens Braun1,3,4,§

  • *Contact author: niklas.zorbach@tu-darmstadt.de
  • †Contact author: klinger@itp.uni-frankfurt.de
  • ‡Contact author: philipsen@itp.uni-frankfurt.de
  • §Contact author: jens.braun@tu-darmstadt.de
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Phys. Rev. D 112, 076036 – Published 31 October, 2025

DOI: https://doi.org/10.1103/nsd5-nxdp

Abstract

Lattice Monte Carlo simulations and the functional renormalization group (RG) are powerful approaches that allow for quantitative studies of nonperturbative phenomena such as bound-state formation, spontaneous symmetry breaking, and phase transitions. While results from both methods have recently shown remarkable agreement for many observables, e.g., in quantum chromodynamics, an analysis of deviations in certain quantities turns out to be challenging. This is because calculations with the two methods are based on different approximations, regularizations, and scale fixing procedures. In the present work, we present a framework for a more direct comparison by formulating the functional RG approach on a finite spacetime lattice. This removes all ambiguities of regularization, finite-size, and scale fixing procedures in concrete studies. By investigating the emergence of spontaneous symmetry breaking and phase transitions in a Z(2) scalar theory in d=1, 2, and 3 spacetime dimensions, we demonstrate at the example of the local potential approximation how this framework can be used to evaluate and compare the systematic errors of both approaches.

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Phys. Rev. D 112, 076036– Published 31 October, 2025
  • Received 26 May 2025
  • Accepted 3 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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