Work

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

Year: 2025

Type: article

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.

Source: Physical review. D/Physical review. D.

DOI: 10.1103/nsd5-nxdp

Authors: Niklas Zorbach, Jan Philipp Klinger, Owe Philipsen, Jens Braun

Institutions: Technische Universität Darmstadt, Goethe University Frankfurt, ExtreMe Matter Institute EMMI

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: Deutsche Forschungsgemeinschaft, Alimentary Glycoscience Research Cluster

Awards: G4199624237, TRR 211: Stark wechselwirkende Materie unter extremen Bedingungen